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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 90, page id 1066518432:0118
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90 DE VIREBUS ET MIOTTDUS CORPORUM. L IB. I.
aequalis sIE angulo FCI _ cum anguli ad i _ F sint (secundum hy-
Pothelin) recti, necesse est, ut tertius tertio atque adeo triangulum
triangulo simile sIF. Secundo, quia angulus gli sub tansente I4 et
secante IO, vel ejus rerticaliter oppolitus aequalis angulo MNI, in
alterno sermento ipsius IM, anguliquo i ec IMN recti Cunt, trian-
sula ipla INM e coli similia existent. Tertio, triangula etiam Tgr.
de C AI similia crune, quoniam angulus qra sub tansente I9 ec le-
cante IA aequatur angulo IC A in alterno segmento, et anguli ad p
ex AIC recti; adeoque tria haec triangulorum similium paria sup.
pedicabune has analosias Ip: Ti = TC: CF, item TI: Ig = NN: IN,
e denique Ig: Ir = AC vel IIY: IC; ergo ex xquo het Ip: IF = MIN.
CF = 2DG: CF = 260: CO.
IV. AdCOGNC, CUM SIE (nuM. TF.) P. C: IF = V (OA. 6O): V (OO. AG)
ex num. TIF. Ip: Ir = 26O: CO, erit Pc = Ip, Si fuerit Y (O A. CO:
OO. AC) =26O: CO; haec ergo rationum aequalitas aNtumatur,
quoniam recta OA ad nullam adhuc magnitudinem est restricta, suam-
que magnitudinem etiam ad diametrum circuli C A relatam habere
debet; Hetque hoc calu OA = 2O6. AC: AO; nec non Ip = Be at-
que adco ip = fe; POrrO (5. 129.) est op = pO. ans. pOg, _ gr = A9.
ang. gAI = A9. 2ang. IC9. Verum quia pg: gr (= Ip: II = TC: CF)
= AC: MC, ideo MC. pg = AC. gr, vel pO. MC. ang. pOg = A9.
AC. ang. gAI = AI. AC. ZICg = AI. AG. IC9, ergo pOg = AI. AC.
TOg: IO. HIC, sed propeer triangula similia OIA _ OOM, crit
TA: MIC =IO: CO =FIO vel RO: CO; propterea ponendo lOco
AI ec MC, homologas proportionales RO e CO, Het an g. pO9
=LO. ACr. ang. ICg: RO. CO = AG. ICg: CO, atque adco om-
nes pog. qui singulis ICg respondent = ACi. omn. ICig: CO = A6.
ang. ICrA: CO, aut posito angulo SOC = omnibus gOp, ACt SOC
AC. IOA: CO, Ceu CO. ang. SOC =AC. ang. ICA, verum
(5. T29.) CO. ang. SOC = arcui SC, _ AO. ang. IOA = arcuiTA;
ergo arcus SC = areui IA, atque BC = AIMC. Tam EOe =IOp =
IOg + gOp; erOO sEOe = (IO9 = sgOp, id est, EO A = IO A + SOC,
sed FOA= FOT +SOC, ErgO FOT FSOC =IOA FSOC, at-
que adeo FOT =IDA; idcirco super diametro SI = C A descrIptuS
Temicirculus SF T cransibit per curra AB punctum L, exitque ac-
CuS SVF = arcui SB, quandoquidem jam arcus AI vel TF ip sI CS,
eE AMIC vel TVS toci CSB aequales FunE OAten(I. PFOPECKCA CUEVa
quaesita in hac Aypothesi particulari BF A est L prerclois quae delcri-
bicur motu puncti in circumterentia circuli SV L Axi E, cum sci-
licet