Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

IN deducendis è propoſitâ generatione curvarum affectionibus etiam-
num progredimur.

_I._ Anguli, qui fiunt ab applicatis & tangentibus ad diverſa curvæ
puncta, ſibimet inæquales ſunt; & minores ſunt illi qui puncto A (ſe@@
vertici) propiores ſnnt.

Tangant rectæ TM, XN; & ad AY parallelæ ſint MP, NQ,
dico fore angulum PMT minorem angulo QNX.

Nam producta recta TM occurret ipſi QN extra curvam pro-
tractæ, puta ad E. Item ipſa XN ſecabit applicatam PM extra
curvam, puta ad H. Manifeſtum eſt autem cùm puncta H, N ſint
ad alias, ac alias partes rectæ ME, rectas ME, NH ſeſe inter-
ſecare inter parallelas PH, QE; quare major eſt angulus externus
QNX interno QET, hoc eſt angulo PMT: Q. E. D.

31.1.

Fig. 26.

_II. Hinc_ poriſmatis _loco habetur_ tangentes ſe interſecare inter or-
dinatim applicatas per puncta contactuum; velut ad F, inter PM,
QN protenſas.

III. Item _angulum PTM angulo QXN majorem eſſe_; (ex
ternum ſcilicet interno.)

IV. Item patet vertici propiores applicatas (proindéque rectas
quaſvis aliis parallelas) cur [?] væ obliquiùs incidere quàm remotiores.

Cæterùm iſta jam olim de _sectionibus Conicis_ oſtenderat _Apollonius_,
ut in edito nuper VI _conicorv [?] m libro_ eſt videre

V. In figura præcedente (poſito applicationis angulum TAY
rectum eſſe, vel obtuſum) _dico curvæ arcum MN rectâ NH, ma-_
_jorem eſſe; rectâverò ME minorem_.

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer