# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/85138403X:0102
# Permalink to this reading: https://leibnizlegible.com/page/85138403X:0102?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 86, page id 85138403X:0102
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=85138403X&page=102
# Source image: https://digitale-sammlungen.gwlb.de/content/85138403X/jpgs/default/00000102.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.90
# 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.

DE C15SOLBC.
TuOHIEU, UE 5 ad T. EpatiUM IBIEUT FCZ AF in luo SicU, aequipon-
derac quincuplo temicirculi in sicu suo, sive in distantia C C su-
spenso; adeoque semicirculo in distantiae CO quineuxla. FF
consequenter (proprer diltantias magnirudinbus reciproce PrO-
Portionales) cum spacium su semicirculi criplum, erie dictantia
distantix suberipla, hoc elt Z C 6, vel 3C F, nempe a recta C a:
Adeoque ZC C vel Z C F a recta F A. Toncundem icaque distat
ictius spacii linea ceneri gravicatis (ec, Ciquod est, iplum gravica-
tiS CenEruM) a rectis illis C a F A. Quod erac oMendendum.
Idem eodem modocolligitur, sumpta ab inicio, aequilibrii
linea F A. Nempe cum series magnicudinumm LZ. sIc V
_ distanciarum D = a3 EIt ex ucrisque composica series memen-
EOruM V D  in D = a: hoc est N a in V: D = a: hoc est
Teries Na in seriem a a inverse ducta; cui conrenit (uE supFa)
ratio r ad 4 D. Mommentum icaque dicti spacii in luo situ (respe-
ctu F A rectX) est ad momentum quadraci F C in distancia FC
Sulpensi, ve 2 ad 4 D; adeoque ad inomentum semicirculi sC su-
Spen(, uc X dd 2: Hlocest, aequiponderat semicirculo suspenso in
diltancia Z F C, hoc est ex puncto C cenero, ho- elt in TuO sIEU.
Cum isicur spacium illud Cissoidale in luo sicu xequiponderae Se-
micirculo in svo, (respectu rectae F A;) Cicque spocium illud Se-
micirculi criplum: Fric aistantia distancia suberipla; hoc eAt
3F C, vel Z F C, nempe a recta F A; Adeoque Z F C, vel ZFC,
a recta C a. Ut prIUS.
Acque hinc Ratim colligimus; Solidum ex conversione dicti
spatii Cissoidalis, ad solidu ex convertione semicirculi, circa can-
dem rectam C a, ese u 5 ad T, (nEPC UE PLANOTUML MOMENCA
respectu ejusdem Ca rectae:) CirCA FCCtAIL AULEM F A (prOPTCF X-
qualia planoru momenta respectu hujus rectae) aequalia esse Colida.
Si quis aurem quaerae, de Polidorum hujusmodi semiconver(.O-
ne factorum, ceneri gravicaris linea, sive ejusdem ab LA vel C a
diltancia: Id eodem plane modo invelligabieur. Duippe cum se-
micxlindricae superticies rectarum I.Z Pemiconrertione Pa Tarum,
Sinc rectarum illarum momentis proxorcionales, hoc est (respestu
recta Ca a) ut V
D= ad Tuorum que cenerorum ab eadem recta,