Clavius, Christoph - Geometria practica

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201171LIBER QVARTVS.

DE AREA MVLTIL ATERARVM
figurarum irregularium.

Capvt IV.

1. FIGVRAS multilateras irregulares, quæ videlicet plura latera habent
11Area multi
lateræ figuræ. inæqualia, quam quatuor, etiamſi valdè irregulares ſint, metiemur, vt
trapezia irregularia, reſoluendo nimirum illasin triangula, & ſingulorũ
triangulorum areas inueſtigando. Nam omnes hæ areæ in vnam ſummam col-
lectæ æquales ſunt areæ totius figuræ propoſitæ. Vt ſi figura ſeptem laterum A-
BCDEFG, reſoluatur in quin que triangula ABG, GBD, DBC, DEF, FDG, ita
22Quando figu-
ra in triangu-
la reſolui po-
teſt, quo m@-
do ei{us} area
colligatur. vteorum latera ſe mutuo non interſecent, in quirendæ ſunt areæ ſingulorũ hoc

129[Figure 129] modo. Quando omnia latera triangulorum nota effici poſſunt per aliquam
menſuram, ſiue figura agrum aliquem repræſentet, ſiue in charta ſolum ſit de-
ſcripta, demittantur ex angulis ad latera oppoſita perpendiculares AH, DI, CK,
DM, FL, ſingulæ in ſingulis triangulis. Deinde in triangulo ABG, 339. triang. re-
ctil. ex tribus lateribus notis ſegmenta B H, H G; & ex his perpendicularis A H, vt
cap. 2. huius lib. Num. 2. declarauimus. Nam AH, in ſemiſſem baſis B G, ducta
producet aream trianguli A B G. Eadem que ratione aliorum triangulorum areæ
perueſtigentur: atque omnes areæ in vnam redigantur ſummam, vt area toti-
us figuræ habeatur. Quod ſi malueris, poteris omnium triangulorum areas in-
dagare ex tribus lateribus cognitis, per ea, quæ capit. 2. Numer. 1. ſcripſimus,
etiamſi neque perpendiculares ductæ ſint, neque ſegmenta B H, G H, in-
uenta.

2. Qvando latera triangulorum interiora menſurarinequeunt, immo ne-
44Quando figu-
ra in triangu-
la reſolui non
poteſt quo mo
do ei{us} area
deprehenda-
tur. que duci, vt non raro accidit in campis, aut agris, qui vel propter arbores, vel
paludes interiectas, rectis itineribus pertranſirinon poſſunt; alia ratione ſco-
pum attingemus, hac videlicet. Cognitis lateribus figuram ambientibus
per aliquam menſuram, inueſtigentur quoque anguli ab ipſis comprehenſi
beneficio quadrantis alicuius in gradus diuiſi. In propoſita figura angulus
C D E, indagandus non eſt, quod ſit extra figuram. Reſoluta deinde figura
mente. aut cogitatione in triangula, ac ſi latera interiora ducta eſſent, vt p@us:

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Scan	Original
71	41
72	42
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75	45
76	46
77	47
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81	51
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83	53
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89	59
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91	61
92	62
93	63
94	64
95	65
96	68
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98	68
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100	70

Scan	Original
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
91	61
92	62
93	63
94	64
95	65
96	68
97	67
98	68
99	69
100	70

Scan	Original
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
91	61
92	62
93	63
94	64
95	65
96	68
97	67
98	68
99	69
100	70