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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 268, page id 1066518432:0296
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268 DE V EREBUS EF MOTTBUS CORPORUM. L IB. II.
TI. Elementum quadrantis 8 aequabitur lincolae BB. Nam 6e:
re velEf =OC: CII = AO: TO = H O: AO, acquicciam BB: Ff =
HO: AO, ergO GB: Ff = BB: Ff, atque adco 6E = BB.
TIT. Figurxe similes boBB et BETV, utpote qua circa candemre.
etam bT constituta, ec e triangulis similibus b0B, BEI, e bBB,
BTV compositae Cunc, praebent analogiam bo: BB vel (nuM. TF. Bu-
jus) C8 aut (nuM. TIT. 5. 463.) ea =EB: TV =EO: TO, atqui
sa: Dd = GFI. (nUM. T. hujuS) OI: Od, et Dd: Dd =Od: OL. vel
OA, erSO ex aequo habetur bo: Dd =EO: AO = AO: TO; atque
2d00 b0. IO = AO. Dd = AO. Cn.
IV. Est vero duplum trianguli BTO =be. TO, duplumque trian-
suli BTO =BF. FO, ergo duplum triansuli BOb = b0. TO (num.
FTI. hujus) = AO. cn, et per consequens eriam arexe B AO duplum
xquabit rectansulum sub AO. DC. Quod erat demonstrandum.
C OR OL L A R F U M I.
465. Ductis ex logarithmicae puncto C ad puncta A et O rectis
CA ex CO, triangulum rectilineum C AO aequabitur ubique homo-
10g0 sectori hyperbolico BAO.
C OR OL E A R F U M TI.
466. Tungatur OI, eaque prOdUCatUE IN P, CTUNEque AP = OD,
ec OP =HD. NTam, quia OS ipE RD normalis cA, crunt anguli
SOR ejusre alternUS APO _ ODR aequales, atque adeo triangula
rectangula AOF SE ORD Similia, Ob laECFA VETO AO SEOR xqua-
lia erunt etiam hxec triangula aequalia, ac proinde AP =OD et
OP = HD. AP autem CA FANSCNS AECUS AR compolIEI CX arCU AC,
CujuS TInUS OFI aequatuE tangenti AF anruli sectOrIS AOB, _ CX
Temissi CR complementi ejusdemt. RF DC eAt l0g-uS ratiOniS DO
ad AO, id est, l0g- us rationis tangentis AP praedictiarcus seu an-
suli compoliti AOR ex angulis AOG _ GOR ad radium scu (i-
NUM EOTUM AO. AEqui ratiO AP ad AO = rationi OR ad TK, id
est, rationi, quam habet radius OK ad tansentem TI Cemislis com-
plementi anguli AOC, cujus sinus aequatur tangenti anguli sectoris
AOB.
dC1.