HHHHfìlMHIMMlM 
42 
i Hi 
lE 
Brevius: Ductae intelligantur Bs, Bh parallelae ipsis CS, CH, 
eritque BAC+BHC=RBs+hBII=HBR — hBs=HBR — IICS. 
Q. E. D. 
Reducto ad puram Geometriam Problemate, in Analysi per 
gere non erit difficile, quam brevitatis gratia omitto. 
VII. Regula pro Constructionibus Mechanicarum per 
Rectificationem Linearum Algeb r aicarum. 
Ponatur indeterminata x, et coordinatarum lineae Algebraicae, 
una Vbx m + cx r , altera yjbx" l + cx r , existente rr m, sequitur 
Analysis Elementi curvae Algebraicae: 
bm . x m_1 +cr.x r_1 dx + bm.x m ~ 1 "+’cr.x r ~ 1 dx 
Liem. Loordm. 
2yjbx m + cx r 
Quadrata Elem. Coordin. 
2 V + b X m _j- c x r i 
bbmm.x 2m ~ a -f 2bcmr.x m + r ~ 2 -f ccrr.x 2 *~ 2 dx? 
4b.x m -f-4c.x r 
bbmm.x 2m—2 —2bcmr.x m + r_2 -f-ccrr.x 2r '~ 2 dx? 
+,4b.x ffl 4T4c.x r 
reducta ad idem nomen et addita faciunt 
pro 1. fòrttì. + b 3 mm. x 3m—2 + bcc rr. x m+2r ~ 2 — 2bccmr. v m+2r—2 
pro 2. form. 
3,.v 3r—2 
■f c 3 rr.x 
+bbcmm. x ,+2m-2 — 2bbcmr. x r+2m — 2 
dx? 
+ 2 b b x 2m + 2 c c x 2r 
factaque divisione per x 2,n , et extracta radice, habetur elementum 
Curvae 
dx>/+ b 3 mm. x m ~ 2 +bccrr — 2bccmr . x 2r_m—2 = / r = 2m 
= ====== posita 
dx V + c 3 rr. x 3r_2m—2 -fbbcmm — 2bbcmr. x r 2 \ m “ r 
V + 2bb + 2cc .x 2 '— 2w 
+ bm.x l/jm ~ 1 dx/ > b 
+ cr. x — '/¡ r -idx/'c 
V^2 yj + b b+cc, x 2m 
factaque divisione per-fbm/’b erit + x' ,iM ~ 1 
4-cr^c. -f-x~ ! 'A*-—i x 
T*- /±bb+ cc.x 2 
alicujus, cujus ordinatae sunt 
x 1 /* m ./ , 2.>/l+x m x l/am .y^2 .Jl— x m 
Bitcrs 
m m 
elementum Curvae 
, x r • .^1 -f-x r x r . v ^2.yj—J+x r 
m secundo casu, una , altera — 1 1 
r r