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

Scan	Original
101	383
102	384
103	385
104	386
105
106	386
107
108	387
109
110	389
111	390
112	391
113	392
114	393
115	394
116	395
117	396
118	397
119	398
120
121
122
123	399
124	400
125	401
126	402
127	403
128	404
129
130

211481SUPER HUGENII EXCEPT. opera detur magis præciſa ex ultimis. At miror, cum Hu-
genius incidiſſet in meam Hyperbolæ approximationem, quod
eam non potuerit Circulo applicare; Nam in Hyperbola abſ-
que dubio 24 prop. approximationem ex ultimis ſimilibus
polygonis conſtruxit: Omnis enim ad Circulum approxi-
matio ex polygonis deducta, Hyperbolæ eſt etiam applica-
bilis, & vice verſa. Sed hoc non videtur animadvertiſſe Hu-
genius; alioqui in fine fuarum Animadverſionum non pro-
mitteret talem Hyperbolicam approximationem, de cujus
applicatione ad Circulum nihil dicit. Quæ autem illic affir-
mat (ſi de ſemet loquitur in plurali) tranſeant; ſi verò etiam
de me adeo fidenter ſibi perſuadeat, falli ipſum putem, cum
hæc eadem quadratura, de qua loquitur, antequam ab eo
videretur, ad laboris dimidium à me ſit reducta.

Ne autem Hugenii praxis geometrica minus peritis videa-
tur noſtram ſuperaſſe, ex noſtra approximatione, ab Hu-
genio rejecta, ſequentem praxin exhibebo.

In fig. Hugeniana ſit A C = A, A B C = B, ſitque
11TAB. XLIV.
fig. 3. A + B: B : : 2B: C; eritque {8C + 8B - A/15} major, quam
arcus A B C; differentia autem, in ſemi-circumferen-
tia minor erit quàm ipſius {1/3500}, in triente minor quam
ipſius {1/40000}, & in quadrante minor quam ipſius {1/300000}. Sed quo-
niam præcedens approximatio major eſt quàm arcus, aliam
addamus eodem minorem. Sit A: B: :B: D; {12 C + 4 B - D/15}
minor erit quam arcus A B C; differentia autem in ſemi-cir-
cumferentia minor erit quam ipſius {1/1000}, & in quadrante
minor quam ipſius {1/60000}, inter has approximationes ſit maxi-
ma, penultima ſex continuè Arithmeticè proportionalium,
quæ minor erit quàm arcus, differentia autem in ſemi-cir-
cumferentia minor erit quam ejuſdem {1/23000}, & in

Page concordance

Text layer

Text normalization

Search

Scan	Original
101	383
102	384
103	385
104	386
105
106	386
107
108	387
109
110	389
111	390
112	391
113	392
114	393
115	394
116	395
117	396
118	397
119	398
120
121
122
123	399
124	400
125	401
126	402
127	403
128	404
129
130

Scan	Original
101	383
102	384
103	385
104	386
105
106	386
107
108	387
109
110	389
111	390
112	391
113	392
114	393
115	394
116	395
117	396
118	397
119	398
120
121
122
123	399
124	400
125	401
126	402
127	403
128	404
129
130

Scan	Original
101	383
102	384
103	385
104	386
105
106	386
107
108	387
109
110	389
111	390
112	391
113	392
114	393
115	394
116	395
117	396
118	397
119	398
120
121
122
123	399
124	400
125	401
126	402
127	403
128	404
129
130