# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/85138403X:0043
# Permalink to this reading: https://leibnizlegible.com/page/85138403X:0043?run=74
# Title: [Johannis Wallisii SS. Th. D. Geometriae Professoris Saviliani Oxoniae, Tractatus Duo] Johannis Wallisii SS. Th. D. Geometriæ Professoris Saviliani Oxoniæ, Tractatus Duo (shelfmark Leibn. Marg. 103)
# Folio 27, page id 85138403X:0043
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=85138403X&page=43
# Source image: https://digitale-sammlungen.gwlb.de/content/85138403X/jpgs/default/00000043.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.92
# 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.

DL CLC LDLLL
xquales utique Z O F. Idem nempe erit cenerum gravicaris
Sectoris Sphaerici GZ2 C, acque segmenti superticiei sphaericae
Segmento Z2C Cimilis ex concentrici radium habentis Z GC. UIF
enim E (punctum medium rectae CY) est centrum gravieatis
Eeomenti Superticiei sphaericxe 22 C (proprer segmenta superfi-
ciei sphaericae segmencis Axis iisdem planis abscistis ubique pro-
porcionalia;) ita Segmenei limilis concenerici radium habentis
CC (cujus lingula puncta, utpore conorum vel prramidum
coridem aequalium Sectorem Sphericum complenrium centra
gravicaris, aequalicer onerari incelligenda TUnE) centrum gravicr
eis eric in suo radico similicer sicum. Quod iptum elt ex centrum
scaricaris Sphaerici Sectoris, Cive preamidum simul onnium nU-
mero insinitarum sectorem illum complencium.
74. Duam superius (530) Tuscepimus ratiOneM, 9 A F 9-
4C Fgad 2 C F 9, odendendum; eam sic inveltigamus. Primo
quidem cum Trilineum CZ A F Z Fg. 1. in Semiercloide (pro- Semierclor-
ocer Semicirculi incerpolicionem incer crilineum illud ejusque dis respecti
axem C F) Ec diltorrum; intelligamus (exempro semicirculo)
trilincum illud restitmi in sicum debicum, procrulis scilicet omnibus dum con-
Z 2 ad rectim C F, uc puncta 2 coincidane punctis Y: dc sic ubi- dersione cir-
que. (Ouod cancundem est atque superticiem curram crilincam eu Axem
FCF Z C tig. 2. in planum expandere.) Duo facto, rectae EJ. falam.
Rc prius inclinaea in Fig. L. erigentur ue in Lig. 7. Exempris
nempe Traperiorum omnium Priangulis (qua Triangulis Semi-
circuli abique aGUAMEuT) minebune cancum Parallelogramma,
Triangulorum illorum dupla: Dura Parallelozrammum V P DB
in Trilineo restiruso, duplum Triangulio F p in Semicirculo, (&
sic ubique:) UEc eadem jam sc racio omnium Z L in hxeC respe
etira Parallelooramma, ad omnes 2 Y in eadem Parallelopram-
ma; acque prius in Cur respectire Triangula, vel horum corum
ve altitudines.
75. Cum, Cumpris Y, y, xoualiter utrinque a CenErO. C TC-
moris, alticudines binae Ly FX simul Cumpex aequent ubique
LC, (IREque Z Y m Y aequales; erie ubique 2 Y X F Y F M Y X
FY = 2 YXFC. Sire, quod cancundem est, quadrilineum
Mu X L una cum quadrilineo Z Er N, complene Parallelogram-
mum basis E altirudinis FC, (altero scilicer supplence quod
in altero deest.) Adeoque perinde est sre ducamius omnia P2-
Fallelogramma
Momentum
Axis,  (0-
7