Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Table of figures

< >
[131] Fig. 12.* 29. Apr.
[132] Fig. 13.* 3. Maii.
[133] Fig. 14.* 6. Maii.
[134] Fig. 15.* 7. Maii.
[135] Fig. 16.* 10. Maii.
[136] Fig. 17.* 11. Maii.
[137] Fig. 18.* 12. Maii.
[138] Fig. 19.* 14. Maii.
[139] Fig. 20.* 15. Maii.
[140] Fig. 21.* 18. Maii.
[141] Fig. 22.* 19. Maii.
[142] Fig. 23.* 20. Maii.
[143] Fig. 24.* c a * 27. Maii.
[144] Fig. 25.c * 31. Maii. a *
[145] Fig. 26.* 13. Iun.
[146] Fig. 27.* 16. Ian. 1656.
[147] Fig. 28.* 19. Febr.
[148] Fig. 29.* 16. Mart.
[149] Fig. 30.* 30. Mart.
[150] Fig. 31.* 18. Apr.
[151] Fig. 32.* 17. Iun.
[152] Fig. 33.* 19. Oct.
[153] Fig. 34.* 21. Oct.
[154] Fig. 35.* 9. Nov.
[155] Fig. 36.* 27. Nov.
[156] Fig. 37.* 16. Dec.
[157] Fig. 38.* 18. Ian. 1657.
[158] Fig. 39.* 29. Mart.
[159] Fig. 40.* 30. Mart.
[160] Fig. 41.* 18. Maii.
< >
page |< < (423) of 568 > >|
150423ET HYPERBOLÆ QUADRATURA. quos terminos æquales appellamus ſeriei terminatio-
nem.
PROP. VII. PROBLEMA.
Oportet prædictæ ſeriei terminationem
invenire.
Ut huic problemati ſatisfiat, oportet primò invenire
quantitatem quæ eodem modo componitur ex termi-
nis convergentibus a, b, quo ex terminis convergentibus
{ca + bd - ad/c}, {bc - bc + ae/c}, hoc autem facile fit hoc modo:
inveniatur
quantitas quæ multiplicata in a &
addita b multiplicata in
quantitatem data m, eandem quantitatem facit ac ſi multi-
plicaretur in {ca + bd - ad/c} &
adderetur {bc - be + ae/c} multiplicata etiam
in eandem quantitatem data\m m.
ſit quantitas illa z, & pro-
inde za + bm æquatur {zca + zbd - zad + mbe - mbe + mae/c}, &
æquatione
reducta invenitur {z = mac - mbe/ad - bd};
quæ quantitas ſive multiplica-
ta in a &
addita m, ſive multiplicata in {ca + bd - ad/c} & addita
{mbe - mbe + mae/c} efficit eandem in utroque caſu quantitatem nempe
{maae - mbae + mbad - mbbd/cd - bd}:
& proinde prædicta quantitas eodem mo-
do componitur ex terminis convergentibus a, b, quo compo-
nitur ex terminis convergentibus {ca + bd - ad/c}, {bc - be + ae/c}.
atque a
&
b quoniam ſunt quantitates indefinitæ poſſunt eſſe quili-
bet totius ſeriei termini convergentes, modò termini con-
vergentes immediatè ſequentes ſint {ca + bd - ad/c} &
{bc - be + ae/c}, &
proinde quantitas {maae - mbae + mbad - mbbd/cd - bd} eodem modo componi-
tur ex quibuslibet totius ſeriei terminis convergentibus quo
componitur ex terminis convergentibus a, b;
& igitur

Text layer

  • Dictionary

Text normalization

  • Original

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index