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# Title: Leibniz-Handschriften zur Mathematik LH 35, 9, 5
# Folio 25v, page id 00068129:0050
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vel pofissimum 3
itaque dato datis duobus numeris AC et LG, unoque loganithmro
AL dantur et ali logarithim AM, aliis numeris datis MB datis.
Cum ergo (ut breviter i ergo ex AS dentur AV per prop. ex AS Spatiis descensu perca
descensibus dentur AV velocitates per pr capor p. descensu
acquisitae per cap. 2 prop. 4. ex et ex velocitatibus quaesitis tempora
insumta per prop 3 A(T) vel TB per p prop. 3. et
insumtu
ex temporibus insuts sTD, spatia directione proje vi projectionis
percursa AM, ( (per cap. 1. prop. 3. ex posita constructione
Loganthmorum.). itaque datis AS dantur AM, et proinde rectam
sulo SAM completo datur punctum D Quod quarebatur
Coroll. 1 tangens curvae adeoque directio mobilis in puncto lineae
projectoriae dato 1P, sic habetur, in producta si opus AS, sumatur 
IS, quae sit ad 1sip ut A.V ad 1M. C (quae datur ex A.M, vel
ope cap. 1. prop. 1) et jutiu ata AD erit langens. D
conll.2. hinc dantur et velocitates, et per consequens vires
acquisitae et residuae descensu, residua a projectione, earumque
rationes inter se, et
Coroll. 3. quin etiam hinc colligi op potest qua opus sit elevatione
hoc est angulo SAM, et qua vi projectionis sed prima velocitate AB
ut linea transeat per datum punctum, seu ut feriatur datum obje–
ctum. Pateto enim tantum opus esse constructione LogaritEmotum.
coroll. 4. relatio inter, X et y habetur ex  prop  exhibente
cap. 2. coroll. 1  vel 2 vel 3 exhibentibus relationem interet
y et F,  et p pro t substituto valore per X invento cap. 1
vide ejus prop. 3 ex roll. 1. vel scholium sub finem capitis
lorole
a. 5. eadem relatio habetur aliter hoc in Alio modo
relto haec  curvae projectoriae naturam exprimens invenitur
per quadraturas hoc modo: X dx dy:: c: v.
C= b. q. b (X. m et  (per, cap. 1. prop. 1. seu per schol. d. C. 1)
et v = taa = n (3: e). et fit fdx: ba b8+. C.
et fit. dx: b. g.b. (X. m) =
ambae hae quadraturae dantur.
Sdy: Sac -ny. et. sit vero