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

Table of figures

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[61] Fig. 5.G L B H D O A E C K
[62] Fig. 7.K F A C D B E H G
[63] Pag. 404.TAB. XLII.Fig. 1.K F M A C D B L E N G
[64] Fig. 3.G R D B H F E N A X C M P Q K
[65] Fig. 2.K A F c S C L E B T G D R d
[66] Fig. 4.K e G P E m B D f R F S H M C A N L Q n
[67] Fig. 5.B C R E G A F M Q D O
[68] Fig. 6.B C H G E A M Q P K D
[69] Fig. 7.B C E G A M P Q K H D
[Figure 70]
[71] Pag. 450.TAB.XLIII.Fig. 4.B A F R P C D E G H I K S L M N O
[72] Fig. 1.F G I K D L E S T O C N H M V R B Q P A
[73] Fig. 2.F G I K D L E S T O C N V R B Q P A
[74] Fig. 5.A C B D E
[75] Fig. 3.A F G I K D L S T E O C N H M V R B Q P
[Figure 76]
[Figure 77]
[Figure 78]
[Figure 79]
[Figure 80]
[Figure 81]
[Figure 82]
[83] TAB. XLIV.Fig. 2.D H A B E F G
[84] Fig. 1.E G N L O I Q P D K M H F A
[85] Fig. 3.B E F A D G C
[86] I. CasusFig. 4.Y Q R C A B M L I K V C O S X
[87] II. CasusFig. 5.R C Y Q A B I L M K V O X S C
[88] III. CasusFig. 6.Q C D Y K L I N M S V B X C A G O
[89] Fig. 7.IV. CasusQ D C A B S L N X M I V Y K C G O
[Figure 90]
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page |< < (490) of 568 > >|
220490CHRIST. HUGENII 82[Figure 82]
II.
DEMONSTRATIO
REGULÆ
DE
MAXIMIS ET MINIMIS.
Ad inveſtiganda Maxima & Minima in Geometricis quæ-
ſtionibus, regulam certam primus, quod ſciam, Fer-
matius adhibuit:
cujus originem ab ipſo non traditam cum
exquirerem, inveni ſimul quo pacto ea ipſa regula ad mira-
bilem brevitatem perduci poſſet, utque inde eadem illa exiſte-
ret quam poſtea vir ampliſſimus Joh.
Huddenius dederat, tan-
quam partem regulæ ſuæ generalioris atque elegantiſſimæ,
quæ ab alio prorſus principio pendet.
Hæc à Fr. Schote-
nio edita eſt unà cum Carteſianis de Geometria libris.
Fer-
matianæ autem regulæ examen quod inſtitui eſt hujuſ-
modi.
Quoties Maximum aut Minimum in problemate aliquo de-
11TAB. XLV.
fig. 1.
terminandum proponitur, certum eſt utrinque æqualitatis
caſum exiſtere:
ut ſi data ſit poſitione recta E D & puncta A,
B, oporteatque invenire in E D punctum C, unde ductis C A,
C B, quadrata earum ſimul ſumpta, ſint minima quæ eſſe poſ-
ſint;
neceſſe eſt ab utraque parte puncti C, eſſe puncta G &
F, à quibus ducendo rectas G A, G B;
F A, F B oriatur ſum-
ma quadratorum G A, G B æqualis ſummæ quadratorum F A,
F B, &
utraque ſumma major quadratis C A, C B ſimul
ſumptis.
Ut igitur inveniam punctum C, unde ductis C A, C B
fiat ſumma quadratorum ab ipſis omnium minima;
ductis A E,
B D perpendicularibus in E D, quarum A E dicatur a;
B D,
b;
intervallum verò E, D, c: fingo primùm G F,

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