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

Table of contents

< >
[71.] _Theor_. IV.
[72.] _Theor_. V.
[73.] _Theor_. VI.
[74.] _Theor_. VII.
[75.] Lect. XIII.
[76.] Æquationum Series prima.
[77.] _Notetur autem_,
[78.] Series ſecunda.
[79.] Not.
[80.] Series tertia.
[81.] Not.
[82.] Not.
[83.] Series quarta.
[84.] Not.
[85.] Series quinta.
[86.] Series ſexta.
[87.] Not.
[88.] Series ſeptima.
[89.] Not.
[90.] Series octava.
[91.] Series nona.
[92.] Not.
[93.] Series decima.
[94.] Series undecima.
[95.] Not.
[96.] Series duodecima
[97.] Series decima tertia
[98.] Not.
[99.] Laus DEOO ptimo Maximo. FINIS.
[100.] ERRATA
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page |< < (59) of 393 > >|
7759 + HK. CN. = AC. KC + AK. AC = AK. KC. verùm eſt
NP
.
CN + AN. CN = NP x AN. CNq. ergò erit AK.
KC : : NP x AN. CNq. componendóque AC. KC : : NP
11Fig. 79, 80. x AN + CNq.
CNq. cum ſit igitur NP x AN = AP x AN
-
ANq.
& AP x AN = ACq - CNq; adeóque NP
x
AN + CNq = ACq - CNq - ANq + CNq;
= ACq
-
ANq.
erit AC. KC : : ACq - ANq. CNq : Quod E. D.
_Coroll_. AK. KC : : AN x NP. CNq.
VI. Etiam hoc _Theorema_ ſubdemus: Si fiat 2 CA. CN : :
CN
.
E. & 2 CK. CN : : CN. F; & ſumatur CQ = E + F;
erit ducta NQ ad CA perpendicularis. vel reciprocè; poſito quòd
ſit
NQ ad CA perpendicularis;
erit CQ = E + F. Nam (ut
hoc
poſterius oſtendamus) quoniam eſt 2 CA.
CN : : CN. E.
&
CN. 2 CK : : F. CN. erit ex æquo perturbatè 2 CA. 2 CK
:
: F. E. vel CA. CK : : F. E. componendóque CA + CK. CK
:
: F + E. E. Porrò quoniam eſt ANq = ACq + CNq - 2 AC
x
CQ;
erit 2 AC x CQ - CNq = ACq - ANq. itaque
(juxta præcedentem) erit 2 AC x CQ - CNq.
CNQ : : AC.
CK
.
hoc eſt ( ob CNq = 2 AC x E) 2 AC x CQ - 2 AC
x
E.
2 AC x E : : AC. CK. hoc eſt CQ - E. E : : AC. CK.
vel
componendo CQ.
E : : AC + CK. CK. erat autem AC
+ CK.
CK : : F + E. E. ergò CQ = F + E: Quod E. D.
VII. Ex iſtis porrò deducetur, ſi dividatur Semidiameter BC in
Z
, ut ſit AC.
AB : : CZ. BZ; punctum Z limes erit citra quem
(reſpectu centri C) nullus hujuſmodi reflexus axem decuſſabit.
Cu-
juſvis
, inquam, radii AN eſto reflexus GN;
axi occurrens in K.
dico fore CK & gt; CZ. Nam ob hypotheſin (permutandóque) eſt AC.
CZ
:
: AB. BZ. igitur (antecedentes, & conſequentes copulan-
do
) AC.
CZ : : AC + AB. CB. quare ( poſterioris hujuſce
rationis
utrumque terminum in æquales AC - AB, &
BC ducen-
do
) erit AC.
CZ : : ACq - ABq. CBq. eſt autem ACq
-
ABq &
gt; ACq - ANq; adeóque ACq - ABq CBq.
&
gt; ACq - ANq. CBq : : AC. CK (è mox oſtenſis hoc) qua-
propter
erit AC.
CZ & gt; AC. CK. indéque CK & gt; CZ:
22Fig. 81, 82. Q.
E. D.

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