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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 504, page id 851387705:0524
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C Y CF O ID F.
Fraverio puncti K, quod ita dividic rectam Z 8, uE st GR ad Z 8, ut 5 ad 9.
(adeos diltancia R k eric ZZ F 3ZY;) In Friangulo, puncti PI, quod ita di-
vidic rectam PZ, uE SIC F IL ad F Z uE 2 ad 3; (adeoque distancia FIh clt ZZ Y.)
Ratio icaque distanciarum est, ut Z7 F 32 Y ad 3 ZY; Cive ut 322 + 32Y ad
22 L; qua si cum ratione planorum 3 ad F componatur, emersit Colidorum catio
ad inricem ut 92Z + 5ZP ad 22Y; sive, ut 5ZY ad 22. l (hoc est, ut 5
ad 2,) acque intuver ut 9ZZ ad 22Y. Ouod quidem cum ubique tiat, ficque
Callem ubique ratio 5Z X ad 22 Y, adeoque ec ominium ad omnes; non autem ca-
dem ubique rario 9ZZ ad 22 Y, sed neque aequalia ubique triangula vF D cir-
Minducta, (quorum s urrumris eller, pro omnibus 92Z ad 22 Y, ponendum
esset 18 ad 2; quia nempe omnes ZZ ad omnes ZY, hoc est crilineum C A F Z
ad semicirculum C ZF, est uc 2 ad F; quum aurem eorum neuerum (t, non licet
SC argVETC;) Praecer racionem illam 5 ad 2, quaerenda est alia ratio; nempe quam
habeat noncuplum omnium Z2. (sire 2. C arcuum Arichmetice proportionalium)
in respectira Priansula vF p, ad duplum omnium 2 Y (sinuum rectorum, eorun-
dem arcuum) in eadem respectire criansula. Hoce (propier criangulorum
5O4
bates aequales) noncuplum arcuum Aricthmetice proportionalium, in reliduorum
sinus versos ductorum (urpote Priansulorum alcicudines;) ad duplum sinuum
rectorum in eoldem linus versos, Hoc est (uc deinceps tulius oltendetur 5 74, etc. )
ut disserentia quadratorum batis A F Se alcicudinis C F, ad 3 quadrati C F, sire ut
DAF = 9C Fg ad 2 C F9. Cui Ei adjunsatur rario 5 ad 2, hoc cAt 5C F9 ad
2CFq; Het D A F9= 4. C Fg ad 2 C F9, ratio solidi ex semieycloidis conver-
tione circa C. F, ad Sphaeram circuli genitoris.
Segmenta 3T. Fodem tere modo etiam de Tolidis ex conrertione segmentorum arguendum.
solidi cir- Dam es hic omnia minura Prapezia segmenti, verbi gratia CZ C F, circumducta:
ca CF. ad omnia minuta Friangula sectoris FZ C. Sic circumducta, circa, eandem rectam
CF: Tunc ut 5 ad 2, acque insuper, uc noncuplum omnium. ZZ. in respectira
Friangula, ad duplum omnium Z Z in eadem criangula: sn ex hoc demum Colido,
auteratur colidum ex convertione Praperii CZ. Y P cirea rectam C F factum; ma-
nebit solidum ex convertione seomenti C. Z. Y circa rectam C Y.
32. Ft pari sere procestu, si demilta recta Z. X rectae C. F parallela abscindi in-
celligatur segmencum Z. X A; istius segmenti cum dimentio, rum ee Colidi inde tacti,
sive convertione circa rectam C F, sive circa rectam Z X, tacile colligitur. Sed
haec inter qualita non Tunc.
sentrum, 33. Ad cenirum gravicacis inveniendum, supponimus ob datas C F, AD, (B. 2
Gravita datam esse circuli quadraturam; adeoque et centrum gravicatis in segmentis. Nam
tis semi-uE, ex dato cencro pravicaris in circuli segmentis, collisi poste circuli quadrat.
cycloidis. ram, jam ab aliis ostentum est; sic vice rersa, ex data quacratura tacile colligicur
Duan-
centrum gravicatis in scementis. (Quod, si opus C, deinceps oltendetur 367.
e SC99.)
24 Ponamus ilaque primo centrum librae in C, de rellam C. F lineam aequilibrii
cum di (librae tranverlam:) Cicque mriutris semicireuli C. P cencrum graricatis punctum
stat a CF. F. (in circuli diamerro basi Cycloidis parallela.) Ouoniam vero momentum se
miercloidis ad momencum semicirculi, respectu linea C. F; est in racione compotica
e
t