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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 80, page id 797435492:0304
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L. E C F. Z.
rum ex jam modo ostentis O T curram DOC cangir; ergo RSip:
TaTA DK S continset.
Notetur eseDCq. DR 9: : 2R: DS.
NTam eAt DCg. DR g = DG. DK-I. DO. DK = R. P +
DT. DS = R. P - ] 2P. DS = 2 RP, PXDS = ZR. DS.
itaque DCg. DR O:: 2R. DS.
Elac autem perinde rera sunc, nec absimili modo demonstraneur.
etiam si projectae a D rectae D A, DO, DF, e 6. pares sine (quo ca-
Ta curra A C F Z Circulus erit, _E C ArVAD K P. Spiralis Archimedaa)
aut d D A continao crescant.
Exinde vero fasile colligitur hoc Theorema:
XIV. SinE duX CUEVX A CS F, D R P ita versus se relatae, ut a de
Tionato in curia DR F puncto D ductis rectis D A, DC (quarum
haCipIaM DR P SCCELINK) SIE semPex OnadraruM ex DK Vuadru-
plum sparii ADC; duct a D HI ad D C. perpendiculari, _ Facto DR.
DO: DCi. DH; COnneXaquE HIR; CRIt H R. CUrYX D R E Per-
pendicularis.
Nam concipiatur linea D OR O, per K transiens, naturaque talis
ue ad illam aD projectae (Cen DK) se habeant in eadem qua spatia ADC
ratione (quales lineas attisimus in proxime superiori) Se lineam
DOK carisat recta R T, linCaM D R P recta KS; conveniant du-
cemhae cum ipta HD punctis T, S; estisitur (e pracedente) D,C9
DRg:: = =. DT. hoc CADH. DR:: DT; hoc eAt (quo-
in r2. hajato AIam C = mOX prxmonstraris DS = ZDF) DH. DK:
DR. D5.
::) DR. DS. Liguet isitur rectam HI R canseni R S perpendicu-
larem esse: . P. D.
Ira Propoliri nostri priore (quam innuebamus) parre quomodo-
cunque detuncti sumus. Cui supplendae, appendiculae instar, sub-
nectemus a nobis uliratum methodum ex C’alculo tansentes reperien-
ei. Ouanquam haud scio, post cor ejusmodi pervulsatas atque pro-
eritas methodos, an id ex ulu sir Facere. Facio saltem ex Amici con-
silio; eoque libentius, quod prae cxereris, quas tractari, compendio-
Ia videtur, ac generalis. In hunc procedo modum.
Sint A P, PMI politione datxe reAxe linex (quarum P M PrOvO-
sicam curram secet in M) _ M Y curram tansere ponatur ad M,
rectam
218. 224