# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0786
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0786?run=74
# 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 766, page id 851387705:0786
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=786
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000786.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 60 lines, status machine
# Lines: 60 recognised, mean confidence 0.82
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

CapV.
Fig. 170 expantam, coneruere Bilineo r S. an Fig, +70. quam Figuram Sinuum Rectorum
272.
curram in luxerticie Crlindei, expansa in planitiem Cuperfieie Curra, CurVX X n a
tiguram Sinuum rectorum terminanci congruere; et parces parribus respectire
Tumpris. Oux pridem monuimus ad prop. 13.
De Calcun eit tadaus.
diximus. Ouippe urrobique ostendetur B0, ipsi BV. linui recto corresponden-
tis arcus AB, hoc est r B, aequalis: _ Sic ubique. Adeoque _ rna semieslipsis
P R OP. XVEII.
6 l L
Si super, AF a Lisura Sinuum rertorum, Arcuumre, Solidum insistat
alcitudinem habens in lingulis bB Sinibus versis, aequalem respecti
vis B0 Sinibus rectis corundem arcuum: Solidum sc constructum,
Friplum eric Semiguadrantalis Ongula semicirculi, aciem haben-
tis Semicirculi Diametrum. FF Partes partium respectire.
Onde; Solidi sic constructi, partiumque ejusdem, cum Magnicudines,
cum Momenta, e Contragraritatis, innocescent.
Nempe, (retentis Srmbolis, ut in proposicionibus aliquot praeceden.
tibus:)
A. C. Solidi Ara, sic constructi; Magnicudo, 2 Pe.: Distantia Ceneri sravi.
caris a plano Ara, is P; momentum correspondens respectur a in pla-
D0 Ara erecto, s R P: Diltantia Ceneri praritaris à planO rqU, 3R;
momentum respectu ra in plano ran crecto, 3 Ra: Diltantia Centri
craritatis a plano super A a crecto, ioP; momentum relpectu Aa
8A38
A. C. Porrionis, ejuldem Solidi, AbBC; Magnitudo, v R2. F 3 5 R: Momentum
A.
resrectu ra in crecto plano Ara, +0 R3 + 25V R 2 + 553 R; distantia
Contri pravicatis ab illo plano, 3C R2 + 3 su. R f 25i
12V R F 5 52
Nomencum
retrectu ra in erecto planoran, 3 v R + 3S R = 3s. v R; distantia
Ceneri pravicatis d plano tan, 42  F 45 R = 5V
6vR +35; Momencum re-
spectu Aa = Z CR3 + a V R2 = 2 sV R2 = has P; diltavcia Ceneri era-
vitatis ab A - 5 e R + 4 av R - suR + 2 a s
4V R F 25
Portionis, ejusdem Solidi, bBr; Masniendo, 2R = v R - 3 s2 X
BR2 = ZsR = : B. R. Momentum respectu plani ara crecti,
R P = = C R. - 1 5VR2 = 5s R; relpectu plani + an erecti, 3 Aa
3VR -
 a 5 v R
352R2 = 552VR; respectu Aa, 8 R P + 3CR = av R2
a s R; distantia Ceneri gravitatis à plavo A ra,
ZRF = 6CR - 65DR = 4
98 R 24 vR - 12 5i d planorani
ab A a
R. Z
8R3 - 4V  = 4 s R + S2V
12R2  6vR = Z5
+ 20CX2 - 8 av R + 250R = 4a5
16R = 8vR = 4. 5
A. T. Portionis ABK; Magnitudo, VR 2 = ZsR = Z V P: Momentum respectu
plani Ara crecti, ZC R3 f+5VR2= 85 R; respectu plani ran erecti
3VR3 = 35 R + 55 vR = 3~ P2 + 5 5 VR; relDeCtU PA, 3V R3 - 3 s R
Es vR = 62 R; relrectu A a = 3C R3 + av R + : 50 R2 = 3 a S R;
distantia
Fi
c