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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 69r, page id 00068195:0137
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Ad Conchoeidem considerandam transsribatur huc figura scholemi ad lib. 2. Geom. Cartes. rag. 252. et 258.
FC In conchoeide ista, polus est G. Norma AB, eaque cumpo prietas, ut omnes
rectae ab ea versus G ductae ut CL. EA, sint aequales. ducatur CB. d applicata
on perpendicularis norinae AB. eique sumatur aequalis CD. (CD = CB) ducaturque DF
aequalis LG (DF = LG) et parallela Ep. recta PFC. erit ad curvam e
perpendicularis. Porro memorabile est, observalum ab Hugenio, si ducatur LH paral
plela EP. dum rectae C P occurrat in H. ac deinde recta HG. angulum HGC esse rectum
Tangens quoque aliter ab a chholenio inventa est, et hoc quidero modo. ducatur LX
parperpendicularis ad CM. et KN perpendicularis ad CG. erit NM parallela
CF tangenti, sive si si N M. NN moducatur dum occurrat ipsi CP. in
Hi = LG. et LH = GI. sH - 5yO. erit
 M. perpendicularis ipsi ep.
Triangulum Characteristicum esto: CQX. Triangula ei similia sunt PCT. (DAG. POM.
CM T. (XET). PMC. (PAR. PHS. D HL R)
multa duci possunt Theoremata memorabila.
vig. CP = me cM Ergo:
CX
C2
qX
CP CQ = Meecs. et.
CBR
Ex his
Quando EAt = PA. conchoeis nascitur ex laagentibus ciiculi. adoc Jac. Greg.
prop. 5. 3 fig. 6.
= M A- B
Cum similia sunt rectangula e KL. et L AG. erit: CL = LK  7G. CK
FG
Ergo CL AG. = LG CB. Ergo Ecce propositionem mermorabilem: quocunque puncto puncto c. in conchocide assumto
AG
Ex
rectangulum ex applicata ad normam, & portione rectae a puncto ad potum ductae infra po inter potum et normant
assrumtae cadentis, semper idem est, quia rectangulo eorum quae semper eadem et et AG. aqvale
Hem CtCK = LGTG id est cylinde omnium CKa aequatur omnibus 1G in TG. vel omnibus LT in HG
demque AG 2TC = CB CK. seu rectangulum TA = rectanguto et
CLTG= LGCCZCK. Cylinder omnium TG= LG,CK. seu onval iet angulo diffeoentrae inter CM. et TG in 2G.
AG CK = TGCB. Cylinder omnium k seu cylinder omnium C M. (quadrabilis) demto cylindio omnium TG = rectansuli
ex TGret CB. a qualis
Cum sit CD = CB. = Am erit DL = E M.
 Triangula similia CBR et CQX. Ergu: A = cB - BR
Cq
X G
rursus eta similia CBR et ALH. fie
 = EB = BK
CA LH - CB n
AL = A HB1
CBERL = LHEBR
CRCQ = CX CBCCX. seu CB ad arcum, (momentum LB arcus e norma) = CQ ad nonmam.
CRAXG = BR CX. seu BR ad arcum, summae omnium et ad altitudinem
CB~Xq = BR Cg. seu BBR ad basin = CB ad altitudinem.
Trianguea similia: RLH et CgX. ideo: KHC  YH= LR Y
x
HR CQ = HL CX. summa omnium HR ad basin = omnibus HL. ad anum
HL autem sic invesrigabimus HL- . Ergu. H1L = Ct G1 Idem aliter: LHHL - G1 + 15. bq. c 
B
Lincarum quantitas ante omnia invesstiganda: A CL. semper eadem - Et (a) AG. sempe eadem (b) Cm. (7.) CB (1)
+
sed quia CB. aliler inveniri potest, posita  pro cognita, ed vicissim, assumamus CM. pro cognita, id est, dponamus
sA  normam divisam in partes aequales infinitas. Manifestum est cum sit CB- Ct
AG
CBEse CB - CL AC ab
EG
resta Ergo ad habendam CB. investiganda est LG.
cP 2G. ab 2G 2G
LG autem inveniemus si CLG iivenerimus. atqui CL G esst Rq CM + AG MGC sed MG = AG+ CB. Ergo MG
AG + CB + 2 AG CB. Ergo CLG = CM + AG + CB + 2 AGCB =. CL + LG. sed LG = CL AG. Ergo
Ergo
= CL + cLAG
2cF CB 
Cm + AG+ CB+ 2AG c0 = CLH + E AG + 2CL eL AG
Cm + A5 + CB + 2AG CB - CL  - 2 C K AG = CL AG Ergo
CM C6+AG 2+ CB + 29G C8 - C L C = 2 CL AG, CB = ci AG ex sac aequatione pendet cognitio ipsius CB. sed hinc
apparet utilius faciliorem longe reddi aequationem, si CB. sumatur procognita CM. pro incognita, fratim
enim talis aquatio oritur: AGCB + CB  + 2AG CB - CL TF - 2CL AG CB - C L’AG  = CM
sed ne in prolssum nimis calculum ind nos induam,, CB sud linearum mostri diagrammatis determinationem,
theoremalis jam inventis utamur.
EA. = CG- LG.
summ
rormam 
urvam
esia
simma omnum A5i
curvam, quadrabilis
F
G eadem
CL. eadem
Cm
D: MA
DL = Cm - cL - cD.
7 GH - YZH = 2G = (CH L CGe vel (CH = cL - 1G = 2CL LGA
a CG= CL E1G= VCM + AG+ CB
y LH = XCH = CL - 2CL
et
CB.
vel
15
52
5. C  Ct - LI - cL
e
 us a  carrunt
LG = 092 - d F - CG. CL.