An Account of Books

VII. An account of Books. 1. Epistola D. Guilielmi Musgrave, S. R. S. ad Editorem missa, in qua ratio redditur libri nuper editi, cui titulus, De Arthritide Symptomatica Dissertatio. Auctore Guilielmo Musgrave, M. D. Inclyti Medicorum Londinensis Collegii, & Regiae Societatis Socio, in 8vo. De Experimentis meis, cum ipsa jubeat Pietas rationem aliquam Regiae me Societati reddere; jam post intermissum aliquamdiu commercium Epistolare redditurum merito expectes. Quare per nuperos hosce dies quid in re Medicâ notaverim, quid etiam lucubraverim, quando ad Scientiam naturalem promovendam, pro tua humanitate id tibi conferre videatur, en paucis accipe. De Arthritide scribentes, quorum ego Libros pervolvi, omnes in eo laborarunt, ut Morbi istius qua Exquisiti, Primarii & Genuini Doctrinam excolant & Disciplinam edant; de Secundariae sine Symptomaticâ Arthritide, parum vel minimè solliciti. Qui quidem eorum Error quodnam extiterit in evincendâ Arthritide impedimentum, quas moras fecerit, quantoq; fuerit Humano Generi incommodo, vel ex eo constat, quòd Arthritis exquista sui generis materia, eaq; sine Morbo praecedente ullo Paroxysmos celebrante, tum etiam propriâ gaudeat Curatione: E diverso manifestum est, Arthritides Symptomaticas, nullam habere sibi peculiarem, sed vel Arthritidis Primigeniae materiam, vel ab aliquo praecedente Morbo, quem Primarium dicitur, derivatam; semper autem a Primario Morbo eas in Paroxysmos evehi, propriasq; Curationes semper semper postulare: Unde palam est, quantum illi fuerint hallucinati, qui dum uni eadem tantum Morbo, nempe Arthritidi Medicinam facere sibi viderentur; revera multis, illoque inter se diversis, diversaque ratione impugnandis facerent. Ut in ista Medicinæ parte quod deest, pro virili suppleam, Arthritidis in Primigeniam & Symptomaticam divisionem, itemque symptomaticæ in suas Species deistributionem, religiosissime ante omnia conservandam propono. Eum recte curaturum credunt, qui rationalem Medicinam profitantur, quem prima Origo Causæ non fefellerit: neque curari id, quod agrum est, posse ab eo qui quid sit ignoret. Quid quod Doctissimum Mortonum in Phthisiologia, non sine Gentis Medicæ approbatione & applausu, distinctione ea utentem legimus; istiusque operâ Morbum difficilem luculententer explicari, gravissimum fœliciter curari. Hunc ego Choragum secutus Arthritidem dico Symptomaticam, in eaque Species, quotquot usquam mihi innovuere, comprehensas. Illius ratio generalis in eo locatur, quòd cum Morbi sint ab Arthritide Primigenià diversi, & intervallo quodam distantès, Stationes Primarias linquant, & erga Arthritidem moventes ei paulatim appropinquent. De appropinquandi modo ut recte cogitemus, Primarii Affectus Exuviae, sive collapsa symptomata, simul cum Arthritidis usurpato Primigeniæ Vultu, Arthritides Symptomaticas certissimè commonstrant. Harum ecce recensionem! Primigenia Falso sic appellata, quae Rheumatismo, Minus proprie dicta, quae Chlorosi, Magis propriè dicta, quae Hydropi, Melancholìæ, Scorbuto, Lui Venereæ Asthamati, Febri, Colicæ, Morbis quibusdam Cuticulæ tribus, Rheumatismo superveniens Symptomatica, fallò & ex vulgantum opinione dicta Arthritìs, Paroxysmos ad morem Arthriticum habet omnino nullos; nec Materiam ei, quae est Arthritica ulìà ex parte comparem, sed a viscidà quadam materia ductus exiguos implente eosque distendente proficiscitur. Quìd huìc ῥαιχθῇ sit in causa exquiritur, & tandem vel a Calore Frigoreque vehementibus & continuis, vel ab Sale Alcalico in sanguine retento, vel ab utroq; eam oriri, tanquam probabile, declaratur. Arthritìs ex Chlorosi eas tantummodo pallidas invadit, quae Miasmate Arthritico sunt hæreditario imbutæ. Chlorosi abiturae supervenit, & simul cum Vultu colorato, cum Robore, cum Sanguinis ἐπιστροφῇ, istorum Symptomatum Societati se immiscens, proflìt Arthritìs. Causam habet conjunctam cum Arthritide Primigenia communem, à Chloroseos causa multum abludentem. Quamdiu vagatur hæc Arthritìs, incerta ejus est Diagnosis; sed ex Ἐγροτα Parentum morbis expiscanda: Articulis affixa Dolore, Tumorè, Rubore, sed & iis pro augmento mensium minutis & declinantibus, se ostendit. Medendi Judicatio singularis & præcipua requirit, ut per Muliebria sanguis expurgetur. Getur; sicq; Chlorosi & Arthritidi simul semelq; occurratur. Haec affinis ea, qua steriles & Catameniis orbatis afficit. Arthritis; excepto quod a vitiosa plenitudine procreata Catharsi, eaq; tum crebro, tum forti, depellenda est. Hydropi quae suppullulat Arthritis, ita se plerumq; habet. Morbo isti, ubi in humido omne vitium, & cum humidì quod abundat jam prius emissum est, maximè verò post Amara & Chalybeaia, succrescendo emergit, & quidem auspiciato. Annos enim elargitur & valetudinem, si non optimum certe desiderabilem: Quare omni ope & industria niti oportebit, ut auxiliis tum ad Hydropem propulsandum, tum ad Arthritidem invocandam idoneis, augeatur ea confirmeturque. Ex Symptomaticis magis proprie dictis, prima utpote a Primigenia Arthritide remotissima, (nam a remotioribus orsi, ad eas, quae magis vicinae sunt, gradatim descendimus) est Melancholica. Alienum id ac ἀναστρέπει, quod in fistula alimentaria spiritus, natura debiles, premendo Melancholi- am peperit, jam in Artus propellitur, & Arthritidem parit Symptomaticam. Clementer ea se fere gerit, neque Paroxysmos adeo atroces habet, ac reliquae ferme omnes; & ea qui tenentur, in pristinum affectum, nempe Melancholiam plerumq; cito revertuntur. Dignoscitur hic Affectus, si Æger diu Melancholia, demum Arthritide laboraverit, & hac quò magis eo remissius illâ, maximè si hoc crebro acciderit. In ejus Prophylaxi, juvat alienum e sanguine amoliri, ejusque in primis viis regerninationi obstarre: tum spiritus levare, languentes suscitare: quod quidem Aqq. purgantibus & Diureticis, Infuso Teæ Chalybeatis, & Cortice Peruano perficiendum. Melancholicae proxima, sed longo proxima intervallo, est Arthritis Ea, qua Scorbutum excipit; Morbus certe apud Damnonios ingenio valde peculiari, propter Scorbuti, ex quo Emanat, ἀπο peculiare. Est enim is Scorbutus veteris istius Lepre, qua Damnonium universum paucis ante seculis perreptando graviter affixit, ἐπιγραφή. Hinc illæ illae frequentes Papulae, Cutis ille pruritus intolerabilis, Color ille flammeus, Fervor importunus, Exanthemata, Lichenes, Squammulae veteris scil. Lepra reliquiarum, Ignis nondum penitus extincti Scintillulae. Mites habet haec Arthritides Paroxysmos, &c (quod ei proprium) Affectus Primarii Symptomata non pauca constanter retinet: Ur ex Scorbuto Arthritico scabie, maculis, Gingivarum vitiis, renitente licet Medicinâ, etiam dolente Articulo insician- tur. Calido isti Scorbuto quae subnascitur, Arthritides sem- per reperitur Calida: τε παλαιός το παλαιός. In Paroxysmo, Materia Articulis impacta blandè foras elicienda. Cane pejus & angue sunt Repellentia. Extra paroxysmum, eva- cuantibus, Materia peccans amandetur, alterantibus corriga- tur, ne repullulet inhibeatur: Horum primum Mercuri- alibus, alterum Antiscorbuticis cum Antiarthriticis una maritatis, Aqq. Diureticis, tertium Digestiviis attentan- dum. Immoderata Venus ab antiquo Arthritidem accersivit, verum maxime ex quo accessit ei Lues. Maturos hæc Symptomatica potissimum invadit. Lui ad Arthritidem ten- denti calcar addit Empericorum Mos ille perniciosissimus, quo Puris suppressioni in curanda Gonorrhæa properè nimis insistunt hi Ardeliones, neglecta vel remissa facta Purgatione. Etsi Luis in Arthritidem mutatio sèpe est in codem corpore, tamen nonnunquam diversa comprehen- dit, cum a Mariti Lue Arthritis in Uxore per concubitum accendatur. Hujus Symptomatica Dolor est Erraticus, & ob aliena ista spicula acutus, nulli certe Arthritidi tam acu- tus, tam cito recidivus, tam simul longius duratus. Quamprimum interciduntur Accessiones, aut multum re- mittuntur, si nulla fuerit evacuatio Materiæ, in caput ea solet transferri, & vel Apoplexian, vel Motus convulsivos excitare. In Paroxysmo Dolor Paregoricis allevandus, sed non nisi cum Cautele datis ne capiti materia impingatur. In vacationibus, a Lue Venerea mutuo sumenda Indicatio: Antisyphiliticis, cum Evacuantibus, tum Alterantibus, languis tuendus, quem in finem aquae prosunt Bathonienses, & in nostra vicinia Bamptonenses. Asthmati succrescit Podagra creberrime Pituitosae maximeq; si Medicinâ, (Catharticis scil. Δραστικάς, & Antiasthmaticis calidioribus) fuerit extimulata. Ejus Materiae diu in Ægroti corpore extitisse, Pituita videlicet involutam, & eum eâ per Sputum και ἐπιφορά externi credibile est. Aliis omnibus Arthritidis speciebus hoc nomine Arthritis hæc Symptomatica Æstate lætatur. Hyeme ab Asthmate superatur sub ejusque larva se abscondit. Propterea quod illius materia frequenti expuitione magnam partem ejicitur, raro Tofos, aut Ulcera, aut Dolorem habet diutinum. In Epicenæ hujus Arthritidos, nunc Pulmonem, nunc Artus infestantis, Curatione in priore statu ut Asthma debelletur, Dolor Articularis excitandus; Venæ sectio vel prorsus omittenda, vel quam in simplici Asthmate oporteret sanguis minori quantitate detrahendus. Catharsis Orgasmum in sanguine facientibus, sed & iis rarius celebranda, ne videlicet Naturam Arthritida recte ταις ἀναγνωστικαῖς desiderantem, alio divertamus Materiam Arthriticam tum expellentia, tum evocantia, tum interne, tum externe adhibeantur. In altero vero statu, quo propria personâ elucet Arthritis, studiosius insistendum, et, si flaccuerit excitanda, si viguerit tuendæ servitudæque. Natura enim ab Asthmate per Arthritida sibi cavet. In ejus dolore Paregorica propter spiritum difficilem, non temere propinanda. In hujus Symptomaticæ Prophylaxi, Ἀποπλησία fæces & reliquias Eccoproticis subinde datis amandare digestivis coctionem perficere, Diætæ rationem aptam prosequi expediet. Febris interdum exquisitæ, eiq; tam intermittenti quam continuæ, tam Συμβολή quam Συμβολή succedit Arthritis; nec quidem modo intellectu difficili, sive per indomitum aliquid & Ἐπεξεργασία in sanguine contentum, eumq; perturbans sive propter obstructas glandulas oriatur Febris. Ratione ortus, Multiplex est hæc Arthritis; temper autem, quo poslimus studio promovenda, nempe ut tenuetur Febris. In hujus Symptomaticae Prophylaxi, Febris cujus ea Germana est & Fructus, habeatur ratio, quae quidem varia requirit diligentener attendenda. Morbus Colicus hac in Regione frequentissimus est; & nunc a Bile, nunc ab acido Pomaceo, nunc a Dyspepsis ortus, Arthritidem habet frequenter Pedisequam. Quae Prosapiæ prius dictæ est, ei medendæ preferenda Indicatio, qua externis quibuscunque materia foras in Artus electetur. Hujus Curationis proprietas habeatur, auxiliis uti tantummodo externis, Cardiaca respuere interna & calida; ne incitata Febre, & mutatâ simul inclinatione Materiæ, Cerebrum ea, (quod jure quasi avito facere solet) aggrediatur. Colicae ex Pomaceo superveniens, Arthritidis dolorem habet valde acutum, in Colicam facile recurrit, iterumq; Arthritidos personam induit, iterumq; deponit; raro Articularum Nodis, Oppilationibus, Ulceribus est signata; quod ex Materiâ, partim per anum usitate exprefsa partim Intestinis affixa, fieri credibile est. Colicam ex Dispositionis ortam, quae sequitur Arthritis, Catharisi fortiore, vel Cardiacis calidioribus solet excitari; & in Colicam iterum mutari, quoties Materia vel in intestina retrocedit, vel in primis viis de novo generatur; quorum alterum saepè & ex facili fit alterum quotidie. In hac Arthritide sanandâ, Medicinam uti decet, nemo unquam exercet nisi Colicam, cui ea subjicitur, ob oculos posterior. Ubi in Poculis erratum, illud deponendum. Quod intus alieni est, per Aqq. purgantes expellendum. Dyspepsia ut tollatur, Coctionis bene & crebro purgandum, Digestivis roborandum. Hujus tituli Symptomaticis hoc commune est, Quod eorum Paroxysmi per Eccoproctica subinde iterata maxime vel praecaventur, vel saltem minuentur; & quod omnium saepissime in affectum redeunt Primarium. Morbis Cuticularibus, quales sunt Achores, Haemorrhoides, Ulcera, succedit aliquando Podagra. In Morbis hisce Primariis, Natura ineptum aliquid extra propellit. Hoc si adaugatum fuerit, Articulis saepe deponitur. Arthritico durante Paroxysmo conquiescunt Afflictus Primarii, fistuntur Evacuationes, exsiccantur Latices; eo ad exitium perdutro, vel paulo post scaturiunt denuo, & quidem tantisper novâ repullulante & urgente dum Materia, praelium redintegretur, & Arthritica revertatur. In Curatione Morbus quicunque fuerit Primarius in totum alendus, Ulcus per Cathæretica, Aethores per Attraheentia, Hemorrhoides per Aloetica internè, per Hirudines externe adhibitas. Habes Libelli nostri Epitomen: Utinam sane ei, quo te studio & affectu prosequor; utinam equa Societatem observantia colo & revereor par inveniatur. Vale in Augmentum Scientiarum, & illius memineris, quod ab Hippocrate scriptum est, Ἀγαθοῖς ἢ Ἄνθρωποις πάντες καὶ Ἀποστολοί. Iterum vale. Ise Damnoniorum. Equinoctio Verno, MDCCCIII. 2. Specimen Lithographiae Helveticae curiosae, quo Lapidès ex Figuratis Helveticis Selectissimi Äri incisi fistuntur & describuntur, a Johanne Jacobo Scheuchzerio, M.D. Figuri, 1732, 8vo. Not only our own, but all the Bodies we converse with and make use of, Animals, Vegetables and Minerals, rise out of the Earth. Which therefore is a Subject of so great Notice and Consideration, much to be wondred the Ancients should have bestow'd so little Time or Thought upon it; and the more because many of them were so exact in the choice of what they were to treat upon. But Georgius Agricola was the first we know of, that about about 150 years ago attempted any thing to purpose on this subject. His living in a considerable Mine Country, and his great converse with Ores and Minerals, gave him a mighty opportunity of advancing this Knowledge: And his Learning and Diligence were both very extraordinary. But the greater part of his Labour was employ'd in setting forth the Ways of working the Mines, of discovering and ordering the Ores of Metals and Minerals, and in endeavouring to ascertain which particular Sorts of them the Ancients meant by their Names, rather than in clearing up the Natural History of them. Not but that he made some Progress in this too, and very great for the time in which he liv'd, when Natural Studies were only in their Infancy: So great that none of the Writers of Fossils since his time have come near him. Indeed the greatest part of them have done little more than copy from his Writings. But of late there hath been such a view given the World of the Extent, the Use and the Importance of this Study, as to have recommended it to the Pursuit of some of the most discerning Naturalists of the Age. Amongst these is Dr Scheuchzer of Zurich, the Author of this Specimen, who along with Real Learning and great Personal Abilities, has shewn a vast deal of Diligence in his Inquiries into this part of Nature. That City has been very happy in producing several, who have bent their Thoughts this way. The works of Conradus Gesnerus, who was one of the greatest Genius of the last Age, and Jacobus Wagnerus's Natural History of Switzerland, are Instances of this. Every body knows what vast Mountains there are in that Country. And Dr Scheuchzer with indefatigable Industry, to say nothing of the Expence and of the great danger of such an Undertaking, has carried his Searches and Enquiries to the Tops of the highest of them. And even there he found variety of Sea-shells, and other Marine Productions. But these have been also observed on the highest Mountains in other parts as well as here; which indeed cannot cannot but be thought a Thing very surprizing and of great Confederation, by all who duly reflect upon it. Along with the Descriptions of the Bodies here set forth, the Author hath caused Icons to be graved of all of them. The chief of the figured Native Fossils he found in this Country, are the Belemnites, p. 25. 44. The Selenita Rhomboidalis, p. 49. and the Fluor Christallinus trigonus, p. 29. He gives a remarkable Variety of the Fossil Coroloid Bodies, ex. gr. Corallium fossile cortice reticulato, d. 14. Retepora seu Eschara maxima Imperati Lapidea, p. 13. Alcyonium tuberosum forma ficus vel quintum Dioscor, p. 17. Fungulus pyriformis Lapideus, p. 6. Astroites, p. 36, 39. Of the Sea Shells that he gather'd on these Mountains, the most considerable are the Nerita, p. 26. Auris Marina Fossilis, p. 58. Umbilicus Marinus, p. 24. Concha Tellinoides, p. 21. Concha Margaritiferae fragmenta, p. 55. Conchula echinata, p. 49. Peitunculus parvus capillaribus striis notatus, p. 23. Peitum dense striatus, ibid. Chamafossilis, p. 55. In this Shell he observes there were discernible the Vestigia of the Muscles by means of which the Animal adhered to the Shell. Nor ought we to omit the Echinus Spatagus, p. 61. The Asteroidea, p. 2. The Entrochi, p. 4, &c. Two Joyns of the Claw of a Lobster struck out of a piece of Stone, p. 27. And a piece of a Shell of a Crab, of that sort that is called the Molucco-Crab, lodged in a very hard sort of Stone, p. 65. 3. De Locis solidis secunda Divinatio Geometrica, in quinque Libris injuria Temporum amissos, Aristai Senioris Geometrae. Autore Vincentio Viviani, Magni Dux Etruriae Mathematico Primario, & Regalis Societatis Londini Sodali. Opus Conicum in Lucem prolatum, Ann. 1701. Folio. The Author Vincentio Viviani, who was 80 years old when this Book was published, and the last alive of the famous Galileos Scholars, was ever since the year 1642 employed by the great Dukes of Tuscany in directing the Fortifications of their Dominions, overseeing their Buildings, the banks of the Rivers, and other publick Works; so that he complained that he had not leisure to prosecute his inventions in Geometry, that he made in his younger days, of which this Book is one. As for his other Works they are these. In the year 1659. he published a Book in folio, intituled, De Maximis & Minimis Divinatio Geometrica in Quintum Apollonii Librum; and he wishes, that as Apollonius's own fifth Book was found shortly after, so Aristaeus's Books may be found after the edition of this. That Divinatio is the reason why this Book, we are now to give an account of, is called Divinatio Secunda. In the year 1692 he published a Treatise in Italian, intituled, Formazione e Misura di Tutti i cieli, in consequence of an Enigma Architectonicum he had, under a borrowed name, proposed in the beginning of that year, in which divers learned men concerned themselves. These are all he has has published in Mathematicks, besides this Book, and two small pieces, containing the solutions of some Problems proposed by French Mathematicians. He dyed at Florence, An. 1703, and left a great many other Works, rather begun than perfect; but which, such as they are, will no doubt be acceptable to the Publick, as coming from one of so great knowledge and reputation in Synthetick Geometry, and Mechanical Learning. In the Preface to this Book he gives an account of Aristaeus Senior Geometra, as far as can be gathered from the Ancients, and of his Writings. This Aristaeus wrote five Books of Conick Sections, which Euclid himself valued so much as to imitate and add to them, as Pappus says. He wrote other Five Books de Locis Solidis, which are these that Vincentio Viviani pretends to restore. Pappus also seems to say that he wrote a History of what had been done in Geometry until his time. And Campanus in an Annotation on Prop. I. Lib. XIV. of the Elements, mentions a Book of Aristaeus, intituled, Expositio Scientiae quinque Corporum, from whence it may be inferred that he was of the Platonick Sect. Tho the Author intended five Books, as Aristaeus had written; yet he has published only three, and seems to despair of ever publishing the other two. Liber I. In quo de locis Ordinationum conicarum Limitibus pertractatur. This Book is divided into five parts. Part I. Are 34 Lemmatical Propositions, where are considerable cases in demonstrating the properties of the Conick Sections from the Regulatrix; Moduli ex Semirecto, ex verticis, ex latibris; and in the Hyperbola from the Asymptotes, Triangulum circumactum a Sympto- tale, &c. all which he there defines. Part 2. Prop. 35. Shews that the Altitudines Normali- um (or the Subnormales) in all the Conick Sections, erect- ed from the points of the Axis, where the Ordinates are erected, are ad Locum planum: And Prop. p. 36 and 37, that the Normales to a right Line and a Circle erected as above (which is ever understood) are ad Locum pla- num; but in the 38 and on to the 42, that the Normales of the Conick Sections are ad Locos Solidos, which he there determines. Part 3. Prop. 43. Shews that in all the Conick Secti- ons and Circle, the Altitudines Normalium super Ramos ex vertice are ad Locum Planum; but from thence to the 49, that the Normales super Ramos ex vertice are ad locos Solidos, which he there determines. Part 4. In the first three propositions from the 50 to the 52 inclusive, he determines the Locus Solidus of the Rami from the Vertex of a Circle, or from an Origine betwixt the Vertex and the Center, or without the Circle. Prop. 53. he shews that the Rami from the Fo- cus of any Conick Section erected to the Axis are ad Locum planum of a right Line there determined. In the following Prop. p. to the 58 he determines the Loci Solici, made by the Ordination of the Rami of a Parabola, drawn from the principal Vertex, and from an Origine in the Axis betwixt the Vertex and the Focus, and below the Focus, and above or without the Vertex. In the next four to the 62 he determines the Loci Solidi made by the Ordination of the Rami drawn from the Origine in the Lesser Axis of an Ellipsis; to wit, either the Vertex, the Center, betwixt the Vertex and Center, or without the Ver- tex. From the 63 to the 68 he determines the Loci Solidi made by the like ordination of the Rami upon the great- er Axis of an Ellipsis. From the 69 to the 77 the like is done done in regard to the *Hyperbola*, where there occurs a greater variety, as it is here managed. The next two Propositions are the like in the opposite Sections, where they superadd any thing to what was before said of one *Hyperbola*. And because a Rectilinear Angle may be considered as an infinitely narrow *Hyperbola*, to wit, whose transverse Axis is a point, in the 80 and last Proposition of this Book he determines the *Locus Solidus*, made by the ordination of the *Rami* to this Angle, from an Origine in its Axis, either within or without the Angle. To this Book he subjoyns an Epilogue, containing some general Corollaries, useful, as he says, toward some things which he intended to publish; as that in a Circle the *Loci Solidi* made by the ordination of the *Rami* from an Origine in the Vertex, or within, are Parabola, which are all Lines like one another; and that the *Loci plani* arising by the ordination of the *Rami* from the Focus of a Conick Section or Circle are strait Lines, which are also like Lines, and so in other cases, that like *Loci* arise from such applications. Part 5. The first two Propositions determine the *Loci Solidi*, arising when the Tangents of the *Parabola*, intercepted betwixt the Section and either the Axis or the Tangent in the principal *Vertex*, are made ordinates to the principal Axis. And the next two determine the *Loci Solidi*, arising when the *Normales*, either to the Section, or to the *Rami*, proceeding from the principal *Vertex*, are made ordinates to the Tangent in the said *Vertex*. **Liber II.** *In quo Loci Ordinatarum potentium Limites indicantur:* In this he treats at large, in 71 Propositions, of the the *Loci* both *Plani* and *Solidi* arising from ordinates upon a strait Line, whose Squares are equal to the summs or differences of the Rectangles and Squares of a Line, and its Segments and other assumed Lines, in all the variety and combinations thereof. Liber III. In quo Loci variarum dispositionum Limites assignantur. Here is the determination of the Loci plani and Solidi that arise from several ways different from the former. For example, if from two given points there be drawn several pairs of strait Lines, whose Squares together be equal to a given Square, the concourse of each pair is in the Locus planus of a Circle there determined. And (the other conditions remaining) if of each pair of Strait Lines one be drawn from a given point, and the other be perpendicular to a given strait Line, the concourse is in the Locus Solidus of an Ellipsis there determined. Afterwards there are several Problems concerning Arithmetical, Geometrical, and Harmonical mean proportionals betwixt two Extreams, and divers Methods for describing the Conick Sections by points. There are also subjoyned several ad-denda to all the preceding three Books. At the end of the Book are Prints of the Orthography and Gate of a Stately House built by the Author Vincentio Viviani at Florence, with the Inscriptions on the front thereof in honour of the French King Lewis XIV, from whom he had an annual Pension for many years: and of the Family of the Great Duke of Tuscany; and of his Preceptor the Famous Galileo Galilei, with a Print of Galileo's Bust in Brass, which is set over the Gate. ERRATA. P. 1581. l. 22. after refract r. vitionfly. Printed for Sam. Smith and Benj. Walford, Printers to the Royal Society, at the Princes Arms in St Paul's Church-yard. 1704.