# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0781
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0781?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 761, page id 851387705:0781
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=781
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000781.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 71 lines, status machine
# Lines: 71 recognised, mean confidence 0.84
# 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.

PTOP. XVII. DeCalculo Centri Cravitatis
Fst A R = ASR minus, Z A R F ~ R2: HoC Cst, Z A R + AS R = v R; l
vel (relticuro valore minuscularum a, 5y) Za R + a sK - VR
Adeoque (momentis per magnicdinem dirilis) Portionis bBa A, distantia cen.
eri gravitatis a bB,
a +=
R = a5
2a = 25
F 2V k
2a. + 25i e ab Aa 
; ec. ab A a = a -
e - a-
2. a  2 5
25
Vel d
Fodem modo ostendetur (proxter bxB = a R = s R,) momentum portionis
bBx respectu bB, (ungulamre correspondentem cujus acies BB,) este = a R = B R2
e respectu rT, za R = as R F B R2: Et Cencri praricanis distanciam a bB,
= 2 BR
a -= 25
_, 2 7 Y _ = 2 4 5  2. B R
Auceriam (propter ABK = a R = 5 R,) momentum porrionis ABV relpectu
BK (ungulamre, correspondentem,) este : a R - v R2; d relpectu A ay L a R
=as R F 2 R =: Centrique graricaris distantiam d B R,
a = 2. a 5. + 2V R
a = 2
EvR. et ab AC
2a = 25
Si vero, ex Portionis bBa A, momenis respectu bB, et Aa; anteratur Paralle.
logrammi BbBa momentum respectu ucriurris (proxter cencrum gravicatis aqua-
liter ab utraque distans:) ITOC eAt, (propter bB = V a = B, ee BB = a, hujus
que semissem ZbB = Z a) E a B = a R - = a v: Tlabetur Seementi ABB, mo-
mentum respectu BB, -Za R F V R= L = a V: de resrectu Aa, == a R  a5 R
=VR2 F = a V: HIoc eAt, Semisumma quadracorum arcuum nibus versis arith.
metice proporcionalibus convenientium, porrionem b B A complentium: Adeoque
hujus duplum, corundem quadratorum Summa. P.F (momenta per magnicudinem
dividendo, hoc es, per = a R + s _ F a 2, ut SB.) Distancia cencer pravicacis
d BB, 3 a -
2V R - a5
2eR + 2a
2VR a5
R; de ab A a, Z a = = 2C R f 2a2
Eu speciatim, Segmenti A d C momentum respectu ds, (proprex v = R), est
R3. Centrique praricatis a ds distantia est R.
Y78.
Solidaque de Semitolicta convertione facta; sune ad respeclivas Vngulas, (ut P
Expius dictum eAt,) ut P, e ZP, ad R. Puta
Solidtum Frilinei Ar a convertione circa + Y tactum, est d P3 + 2 R2 P; de
Circa A a, 5∞3 - 2 R = Y
Solidum Porcionis bBa A convertione cirea BB Factum, clt. 3 a P F v R P; &
circa Aa, = a P = a 5P = v RF
Solidum Porcionis bB, convertione cirea bB tactum, ell. = ae P = B RP; de
Circa FF, Z02 P = a5P F BRZ
Solidum Porcionis A BK convertione circa B K tactum, elt : a P - v R Z:
_ CirCa Aa = a P = a5 P = VRF
Solidumque Segmenti A b B convertione circa Bb K factum, cst. - 3 a P f. v RP
2i e eirea Aa = = a P + a5P = v RP +  
2.k
2 DE
Et Semisolida, horum semistes.
Si vero libeat haec Ouadrilineorum, et Sectotu corsespondencium, momenta L
respectu Aa incer se comparare; (praeterquam quod illud jam Factum ests dum
VETOrumquE MOmenta danEUE;) Dicendum est, Momencum Ouacrilinoi bBa A
respectu sibi adjacentis Aa ad momencum Sectoris B a A respectu A. a adjacenns
sibi; else uc, omnes BB (illud complentes) in respectiras BC (complentes a BiC
Friangutum;) ad casdem bB in respectirarum B. (complentium a po Frilineum)
Triencem. Hoc est, ue Omnia rectangula bB6 (eo spectantia) ad PrienLCM
omnium bBv. HIoc est, ve Omnia ab, ad Omnia Z sB.
Ouippe Priangula sinouta ut a B (Sectorem complentia) sunt (quoact magni-
iudinem) ad correspondeniia Parallelozramma bB (Quacrilineum complentia)
D dddd