Barrow, Isaac - Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

Scan	Original
231	38
232	39
233	40
234	41
235	42
236	43
237	44
238	45
239	46
240	47
241	48
242	49
243	50
244	51
245	52
246	53
247	54
248	55
249	56
250	57
251	58
252	59
253	60
254	61
255	62
256	63
257	64
258	65
259	66
260	67

311118 dinatam BDin I, & lineam RSin X) ſit MP. ME: : VG. IX;
vel, ſit linea AL talis, ut ductâ MPY ad BDparallelâ (quæ ſecet
axem ADin P, & lineam ALin Y) ſit PE. ME: : VG. PY; erit
11Fig. 177. tunc utrumque _ſpatium_ (ſingillatim) BRS D, vel ADL duplum _ſu-_
_perfici@i conicœ_, quod ex recta per V & curvam AMB mota progene-
ratur.

Nam ſumatur MNindefinita curvæ particula; & per N ducantur
rectæ NOKTad ipſam AD, & NQZ ad BDparallelæ (quæ li-
neas expoſitas, ut _Schema_ monſtrat, ſecent) connectantúrque rectæ
VM, VN. eſtque MO. MN: : MP. MF: : VG. IX. quare
MN x VG = MO x IX = IK x IX. Item eſt NO. MN: : PE.
ME: : VG. PY. unde MN x VG = NO x PY = QP x PY.
Eſt autem MN x VG duplum trianguli MVN. quapropter tam IK
x IX, quàm QP x PY duplum eſt _trianguli_ MVN. pariter autem
ubique fit. ergò conſtat Propoſitum.

Exemplum.

Sit curva AMB _byperbola æquilatera_, cujus _Centrum_ C, ſitque
22Fig. 177. CV = CA = _r._ & CP = _x_ (nam hujuſmodi _calculo_ plerunque
rem expedit peragere) tum connexâ MC; patet eſſe EC = {_rr_/_x_};
& MCq = 2 _xx_ - _rr_ (nam PMq = _xx_ - _rr_) item eſt MCq.
CPq: : MEq. MPq; hoc eſt MCq. CPq: : ECq. CGq. hoc
eſt 2 _xx_ - _rr_. _xx_: : {_r_4/_xx_}. CGq = {_r_4/2 _xx_ - _rr_}. quare VGq = {_r_4/2 _xx_ - _rr_} +
_rr_ = {2 _rrxx_/2 _xx_ - _rr_} = {VAq x CPq/MCq}. vel VG = {VA x CP/MC}. quare
VG. VA: : (CP. MC): : MP. ME. hinc conſectatur in hoc
caſu, quum ubique ſit IX = VA, _lineam_ RS fore _rectam_; & _rectan-_
_gulum_ BRSD _ſuperficiei conicœ_ AMBV _duplum eſſe._

Cæterùm hoc _elegans exemplum_ ſuppeditavit Generoſus, ingenio ac
eruditione præſtans, Vir (_Collegii noſtri, quod olim Sociorum Com-_
_menſalis incoluit_, ornamentum) D. _Franciſcus Feſſopius_, Armiger;
cujus in hanc rem perquam ingenioſo mihi comiter impertito ſcripto
(ipſius injuſſu quidem, at ſpero non ingratiis) ſeu _Gemmâ_ quâdam au-
debo mea condecorare.

Page concordance

Text layer

Text normalization

Search

Scan	Original
231	38
232	39
233	40
234	41
235	42
236	43
237	44
238	45
239	46
240	47
241	48
242	49
243	50
244	51
245	52
246	53
247	54
248	55
249	56
250	57
251	58
252	59
253	60
254	61
255	62
256	63
257	64
258	65
259	66
260	67

Scan	Original
231	38
232	39
233	40
234	41
235	42
236	43
237	44
238	45
239	46
240	47
241	48
242	49
243	50
244	51
245	52
246	53
247	54
248	55
249	56
250	57
251	58
252	59
253	60
254	61
255	62
256	63
257	64
258	65
259	66
260	67

Scan	Original
231	38
232	39
233	40
234	41
235	42
236	43
237	44
238	45
239	46
240	47
241	48
242	49
243	50
244	51
245	52
246	53
247	54
248	55
249	56
250	57
251	58
252	59
253	60
254	61
255	62
256	63
257	64
258	65
259	66
260	67