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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 227, page id 175905688X:0249
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=249
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COMMLEHZARLE EN LTDRUMII.
227
COnCUTTAnE rectX A L, C B, Cubicunque holce aequales angulos
ad polirione datas constituentes) in punctum I. Deinderatio,
quam HIF ad F C serrare debet, detur uc A L’ad K, vel li non ita
detur, ad hanc formam reducatui.
Resolurio. Putatactum esse, quod guaeritur, ponaturque B C ∞q.
AI∞r, H ∞s, B I∞F, _ B F∞ x. Unde, cum proprertriangulo-
rum BIA, B F FI similicudinem, B PHE ad F A, hoc Cst, tadr, liCUE
BF seux ad P. FI, erit F. II ∞. Deinde quoniam A P est ad R,
hoc est, r ad s, sICur HIF ad F. C, Sire - ad g f ∞: Crit pFO-
ductum sub extremis rg. Frx, aequale producto sub mediis 
Ac proinde li utrinque diridatur per r, acque mulciplicetur per t,
aequatio erit (x = + ~ ∞ F9. HIOc eA, rerocata ae qualitate ad pro
portionem, crituts = t adt, icag ad x. Undetalis emersit Con-
structio. Fiat, ut exceNuS, quo R excedit B L, ad B I; ita B C ad BF.
TUI per E ducatur P. d ip(I A B seu C D parallela (ut in prima
FI∞.); aIIE ex D per P agatUF recta D F indefinite (ut in secunda
Fg.): Dico li ex quolibet ejus puncto, ut e, ad positione datas
AB, CD, dua ducantur rectae linex eh, ec in datis angulis Fd C,
hoc est, ipsis AI, IC parallela, dictas lineas datam inter le ratio-
nem serraturas, hoc est, Betore ad ec, (Icur A Iad K, seur ads.
Demonstratio. Ouoniam enim elt, ut excessus, quo R excedit
BI, adBI, ita B C ad B F: erit quoque componendo R ad B I,
SICUE C F ad P B. EInde cum ratiO C F ad E B COIPOLICA SIE CX
ratione CF ad F FI, _ ex ratione ITF ad P B Peu A L ad TB: Crit
quoque ratio K2 ad B I ex eildem rationibus compolica. Podemm
modo, quoniam item ratio R ad B I componitur ex racione R ad
AI, _ exratione A Tad TB: cricratio compolica ex ratione C L
ad FH, e exratione A Lad IB, eadem cum ratione, quae com-
ponitur ex R ad AI, 8 ex AI ad IB. Ouare si communis aute
racur ratio AIad IB, erit quoque reliqua ratio C F ad F II Ca-
dem reliquae rationi R ad AI, scusadr. Ouod eractaciendum.
Fadem estratio ubicunque tandem in recta d P. punctum e astu-
matur Unde manifectum Ec, punctum quaesicum e rectam lineam
concingere DE, policione datam, ac proinde in loco plano esfe.
Omicto reliquos hujus quaectionis calus, cum a quoris ad horum
imitationem facile construi possine.