Clavius, Christoph - Geometria practica

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7949LIBER PRIMVS.

XVI. ANGVLOS OMNES TRES.
Ex tribus omnibus lateribus perueſtigare.

1. Ducta ad maximum lat{us} perpendiculari ex angulo oppoſito (vt ni@irum 1111. triang.
rectil. pendicularis ſemper intratriangulum cadat) inueniantur per problema 9. ſegmenta duo
@aximi lateris facta à perpendiculari. Deinde.

22
Vt minimum \\ lat{us} # ad ſinum \\ totum: # ita min{us} ſegmen- \\ tum maximi late- \\ ris # ad ſinum complementi \\ anguli medi@ lateri \\ oppoſiti.

Rurſus.

331. triang.
rectil.44
Vt me- \\ dium \\ lat{us} # ad ſinum \\ totum: # ita mai{us} ſegmen- \\ tum maximi la- \\ teris # ad ſinum complementi angu- \\ li medio lateri oppoſiti.
551. triang.
rectil.

Inuentis duobus angulis ad maximum latus, qui medio lateri, & minimo
opponuntur; ſi eorum ſumma ex ſemicirculo dematur, reliquus fiet tertius an-
gulus lateri maximo oppoſitus.

2. In Iſoſcele, ducta perpendiculari ad baſem , quam bifariam ſecabit,

66Schol. 26.
lib. 1. Eucl.77
Vt alterum \\ laterum æ- \\ qualium # ad ſinum \\ totum: # ita ſemiſſis \\ baſis # ad ſinum complementi vni{us} \\ angulorum æqualium ad ba- \\ ſem.

Summa duorum angulorum æqualium inuentorum ex ſemicirculo detra-
cta, reliquum faciet tertium angulum.

3. In æquilatero triangulo dabuntur anguli, etiamſi latera non dentur, eum
quilibet gradus 60. tertiam videlicet partem duorum rectorum, vel duas tertias
partes vnius recti, complectatur.

XVII. PERPENDICVLAREM IN LATVS
quodcunque ex angulo oppoſito cadentem.
Ex tribus omnibus lateribus efficere notam.

Per problema 9. inquirantur ſegmenta lateris facta à perpendiculari. Deinde diffe-
rentia inter vtrumuis ſegmentum, & lat{us} adiacens ducatur in ſummam eiuſdem ſeg-
menti, & lateris adiacentis. Radix namque quadrata numeriproducti perpendicula-
rem quæſitam indicabit.

In triangulo enim A B C, ſit A B, 10. A C, 17. & B C, 21. inueſtiganda{q́ue} ſit perpen-
dicularis A D. Per problema 9. reperi{et}ur ſegmen-

14[Figure 14] tum B D, 6. & C D, 15. Differentia inter B D, &
A B, eſt 4. quæducta in 16. ſummam rectarum B D
& A B, faci{et} 64. cui{us} radix quadrata 8. d{at}
perpendicularem A D. Quod quia in noſtro tra-
ctatis triangulorum rectilineorum demonſtratum
non est, demonſtro hoc propoſito Theoremate.

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Scan	Original
61	31
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65	35
66	36
67	37
68	38
69	39
70	40
71	41
72	42
73	43
74	44
75	45
76	46
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Scan	Original
61	31
62	32
63	33
64	34
65	35
66	36
67	37
68	38
69	39
70	40
71	41
72	42
73	43
74	44
75	45
76	46
77	47
78	48
79	49
80	50
81	51
82	52
83	53
84	54
85	55
86	56
87	57
88	58
89	59
90	60