Page:Organum mathematicum libris IX. explicatum (1668).djvu/260 - Revision history

Irene Pedretti at 10:53, 7 October 2020

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Ginevra Crosignani at 16:16, 24 April 2020

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Not proofread: Created page with "In L, deinde in F; interefect ea latus B C in puncto E, abscindatque partes. B E &. Considera duo triangula A B E, A L F, et dic per Regulam auream: ut E B 6, ad B A 12, ita A..."

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<noinclude><pagequality level="1" user="Ginevra Crosignani" /></noinclude>In L, deinde in F; interefect ea latus B C in puncto E, abscindatque partes. B E &. Considera duo triangula A B E, A L F, et dic per Regulam auream: ut E B 6, ad B A 12, ita A L 15, ad L F. Reperies, facta operatione, pedes 30 ut antea.
<center>ANNOTATIO I.</center><br>
''Ex dictis Capite pracedenti §. 2. Constat, in proposito situ Quadrati stabilis, latus B C esse umbram rectam, et latus C D umbram versam. Quoniam igitur distantia K G est major quam altitudo G F, distantia vero I G est eidem aequalis, distantia denique H G st minor eadem altitudine G F; patet, quando Regula dioptrica in Quadrati stabili cadit in aliqua distantia in angulum C. alitudinem esse aequalem distantiae : quando vero cadit in latus rectum B C, altitudinem esse majorem distantia: quando denique cadit in latus vresum C D, altitudinem minorem esse distantia.''
<center>ANNOTATIO II.</center><br>
''Si latera Quadrati divisa sint in 100 partes, et statione K Regula dioptrica abscindat D E 50 partium, in statione I cadat in angulum C, in statione H abscindat B E 50 partium; invenitur ubique altitudo F L 30 pedum ut antea. Nam si dicas in statione K, ut A D 100, as D E 50, ita A L 60 ad aliud; multiplicesque 60 per 50, et productum 3000 dividas per 100; invenies in Quoto 30. Si in statione I dicas: ut A D 100, ad D C 100, ita A L 30 ad aliud; invenies operatione facta iterum in Quoto 30. Tantundem invenies, si in statione H dicas, ut E B 50, ad B A 100, ita A L 15 ad aliud.''
<center>ANNOTATIO III.</center><br>
''Si umbram rectam B C 50 partium, qua in statione H abscindit Regula dioptrica ex latere B C, convertas in umbram versam, ut fiat triangulum A D M et dicas per Regulam auream, ut A D ad D M, ita A L ad aliud; adhuc invenies altitudinem L F 30 pedum. Quomodo autem reductio fiat, docuimus capite preacedenti §. 3. Nempe sit umbra a reducenda ad totum latus Quadrati, ita idem latus Quadrati ad aliud. Itaque si latus Quadrati''<noinclude><references/></noinclude>

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	<center>ANNOTATIO III.</center><br>		<center>ANNOTATIO III.</center><br>
	''Si umbram rectam B C 50 partium, qua in statione H abscindit Regula dioptrica ex latere B C, convertas in umbram versam, ut fiat triangulum A D M et dicas per Regulam auream, ut A D ad D M, ita A L ad aliud; adhuc invenies altitudinem L F 30 pedum. Quomodo autem reductio fiat, docuimus capite preacedenti §. 3. Nempe sit umbra a reducenda ad totum latus Quadrati, ita idem latus Quadrati ad aliud. Itaque si latus Quadrati''		''Si umbram rectam B C 50 partium, qua in statione H abscindit Regula dioptrica ex latere B C, convertas in umbram versam, ut fiat triangulum A D M et dicas per Regulam auream, ut A D ad D M, ita A L ad aliud; adhuc invenies altitudinem L F 30 pedum. Quomodo autem reductio fiat, docuimus capite preacedenti §. 3. Nempe sit umbra a reducenda ad totum latus Quadrati, ita idem latus Quadrati ad aliud. Itaque si latus Quadrati''
		+	[[Category:AKC Works pages]]
		+	[[Category:AKC Pages]]
		+	[[Category:Organum mathematicum (1668)]]

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-In L, deinde in F; interefect ea latus B C in puncto E, abscindatque partes. B E &. Considera duo triangula A B E, A L F, et dic per Regulam auream: ut E B 6, ad B A 12, ita A L 15, ad L F. Reperies, facta operatione, pedes 30 ut antea.
+in L, deinde in F; interefect ea latus B C in puncto E, abscindatque partes. B E &. Considera duo triangula A B E, A L F, et dic per Regulam auream: ut E B 6, ad B A 12, ita A L 15, ad L F. Reperies, facta operatione, pedes 30 ut antea.
 <center>ANNOTATIO I.</center><br>
 ''Ex dictis Capite pracedenti §. 2. Constat, in proposito situ Quadrati stabilis, latus B C esse umbram rectam, et latus C D umbram versam. Quoniam igitur distantia K G est major quam altitudo G F, distantia vero I G est eidem aequalis, distantia denique H G st minor eadem altitudine G F; patet, quando Regula dioptrica in Quadrati stabili cadit in aliqua distantia in angulum C. alitudinem esse aequalem distantiae : quando vero cadit in latus rectum B C, altitudinem esse majorem distantia: quando denique cadit in latus vresum C D, altitudinem minorem esse distantia.''