Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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lum æqualem angulo
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BAD,
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ſecundum
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FTH
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capiat angulum æ
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qualem angulo
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CBD,
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ac tertium
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FVI
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capiat angulum æqualem
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angulo
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ACE.
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Deſcribi autem debent ſegmenta ad eas partes li
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nearum
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FG, FH, FI,
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ut literarum
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FSGF
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idem ſit ordo circula
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ris qui literarum
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BADB,
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utque literæ
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FTHF
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eodem ordine cum
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literis
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CBDC,
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& literæ
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FVIF
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eodem cum literis
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ACEA
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in or
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bem redeant. </
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>Compleantur ſegmenta in circulos integros, ſitque
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P
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centrum circuli primi
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FSG,
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&
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Q
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centrum ſecundi
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FTH.
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Jungatur
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& utrinque producatur
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PQ,
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& in ea capiatur
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QR
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in ea ratione ad
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<
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PQ
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quam habet
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BC
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ad
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AB.
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Capiatur autem
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QR
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ad eas partes
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puncti
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Q
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ut literarum
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P, Q, R
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idem ſit ordo atque literarum
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A, B, C:
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centroque
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R
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& intervallo
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RF
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deſcribatur circulus quartus
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FNc
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ſecans circulum tertium
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FVI
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in
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c.
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Jungatur
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Fc
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ſecans
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circulum primum in
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a
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& ſecundum in
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b.
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Agantur
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a G, b H, c I,
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&
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Figuræ
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abc FGHI
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ſimilis conſtituatur Figura
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ABCfghi:
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Eritque
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Trapezium
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fghi
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illud ipſum quod conſtituere oportebat. </
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LIBER
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PRIMUS.</
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<
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>Secent enim circuli duo primi
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FSG, FTH
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ſe mutuo in
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K.
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Jungantur
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PK, QK, RK, a K, b K, c K,
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& producatur
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QP
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ad
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L.
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Anguli ad circumferentias
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FaK, FbK, FcK
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ſunt ſemiſſes an
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gulorum
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FPK, FQK, FRK
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ad centra, adeoque angulorum
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illorum dimidiis
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LPK, LQK, LRK
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æquales. </
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<
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>Eſt ergo Figura
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PQRK
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Figuræ
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abcK
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æquiangula & ſimilis, & propterea
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ab
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eſt
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ad
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bc
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ut
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PQ
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ad
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QR,
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id eſt, ut
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AB
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ad
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BC.
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Angulis inſuper
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FaG,
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FbH, FcI
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æquantur
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fAg, fBh, fCi
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per conſtructionem. </
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<
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>Er
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go Figuræ
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abcFGHI
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Figura ſimilis
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ABCfghi
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compleri poteſt
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Quo facto Trapezium
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fghi
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conſtituetur ſimile Trapezio
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FGHI
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& angulis ſuis
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f, g, h, i
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tanget rectas
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ABC, AD, BD, CE
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q.E.F.
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Corol.
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Hinc recta duci poteſt cujus partes, rectis quatuor poſi
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tione datis dato ordine interjectæ, datam habebunt proportionem
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ad invicem. </
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<
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>Augeantur anguli
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FGH, GHI
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uſque eo, ut rectæ
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FG,
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GH, HI
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in directum jaceant, & in hoc caſu conſtruendo Proble
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ma, ducetur recta
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fghi
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cujus partes
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fg, gh, hi,
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rectis quatuor po
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ſitione datis
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AB
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&
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AD, AD
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&
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BD, BD
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&
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CE
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interjectæ, e
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runt ad invicem ut lineæ
<
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type
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FG, GH, HI,
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eundemque ſervabunt or
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dinem inter ſe. </
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<
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