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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 89, page id 1066518432:0117
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1066518432&page=117
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine
# Lines: 45 recognised, mean confidence 0.83
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# After the first blank line: the recognised lines in reading order, one per line.

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DE VIRTBUS ET MOTIDUS CORPORUM. L LB. I. 89
PROPOSITIOZXIZ. PRODLEMA.
18I. Si scala solicitationum eravitatis centralium fuerit linea recta FiS. A2.
ha, quae deorsum producta transeat per centrum solicitationum era-
vitatis; invenire isochronam BF. A in hac hypothest.
Ouia (5. 272.) AIR = 2. TIAah = (HIO = AO2). AA: AO PTOPECE
trapezium HIAah, curra AR invenitur hyperbola enc, in qua HIR.
AO: Aa =FIO =AO2
TI. Ex aliquo axis puncto C, tanquam centro, descriptus circulus
AMIN ab arcubus concentricis indetiniteque ricinis FHI, ek lecc
cur in punctis I X g actisque CZ centro C ad haec puncta radiis GI
et Cg, cum etiam rectis AI et AG, illa seu AI secet arcum et in
litque arculus gr centro A delcriptus, junsanturque demum
10, g0 ee pO.
Jam in triangulo TGO, si CO consideretur instar baseos, erit ut
supra (5. L7L.) octensum IO. AO + TO. AC = AP2. CO + GA. AO.
GO, atque adco AP. 6O =IO2. AC + IO2. AO = GA~. AO = AO2
AO = TIOE. AC = AO. AC, et per consequenS TIO -AO2 = AI7
CO: AC (rel num. T. hujus) =FIR2. AO: A2; hinc Het IIR:
AI = Aa. GO: AC. AO, et (5, 172.) AEE: HIR= (=NN: I) =OA.
OA: OO. Aa, erSO ex aequo e per compositionem rationum Het
AFE: AP = Aa. GO. OA. OA: AO. AO. OO. Aa = DA. (1O: OO. A6,
hinc AE: AT =Y (OA. CO): Y (OO. AC) atque adeo eA Curra AF.
adhomolosam AI in dataratione, ac propterea Pe: Ir =Y (OA. 6O):
(DO. AC
TII. Ergo inter circulos concentricos FFI sc egK ad punctum I
aptandta esset quaedam lineola, quae sit ad Ir, diferentiam inter sub-
tensaS IA ec gA, in data rationC Y (O A. (50) ad Y (OO. AC). VC
rum quia facile ridetur esse Ip portiunculam subtenlae AI à PEX-
fatis circulis concentricis interceptam ad praedictam subtenlarum
differentiam Ir in data ratione duplae CFD ad CF, demissis scilicet Cx
punctis  e C Derpendicularibus ad lineam OI productam, vel
duplae CO ad CO; elementum erso currae De lincolae Ip aequale
Doni potest ex eo ipso, quod Ip et De habeant ad Ir datam ratio-
nem; quod respectu rationis Ip ad Ir ita ese demonstrandum cst. A-
GantuT MC, TC, _ MN, quo facto, erunt primum triangula Ipi
ec CTF similia, quandoquidem angulus CIA in Cemicirculo rectus
efficit, ue duo pli et CHH simul rectum requent, uc adeo angulus pli
xqua