Apollonius <Pergaeus> - Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

Scan	Original
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72

10466Apollonij Pergæi ad G F, vt latus tranuer ſum ad

84[Figure 84] rectum, & ducatur ex E recta
E H parallela F A, quæ ſecetur
à rectis D K, G I ad axim per-
pendicularibus in K, & I, &
per D ducatur hyperbole D B
114. lib. 2. circa aſymptotos H I G, occur-
ret hyperbole A B (vt in Prop.
59. 62. 63. oſtenſum eſt) ali-
cubi, vt in B, coniungatur rect a
linea B C, quæ occurrat axi in
L, & ipſi E H in M, duca-
turque ex B perpendicularis ad
axim eum ſecans in N, & re-
ctam E M in H. Dico, quod B L eſt linea breuiſsima.

C E ad E F, nempe K D eſt, vt D G ad G F, & c. Quoniam ex conſtru-
22b ctione C E ad E F, ſeu ad ei æqualem K D, in parallelogrammo D E, eſt vt
D G ad G F, ſcilicet vt latus @ anſuerſum ad rectum, eſtque K I ad I E, vt D
G ad G F propter parallelas D K, G I, F E; ergo vt prima C E ad ſecundam
D K, ita eſt tertia K I ad quartam I E, & propterea rectangulum C E I ſub
extremis contentum æquale eſt rectangulo D K I ſub intermedĳs compræhenſo;
eſt vero rectangulum B I æquale rectangulo D I cum compræhendantur ab hyper-
bole D B, & aſymptotis H I G; ergo rectangulum C E I æquale eſt rectangulo
3312. lib. 2. B H I; & propterea B H ad C E, nempe H M ad M E (propter ſimilitudinem
triangulorum B H M, C E M) eandem proportionem habebit, quàm E I ad I
H, & componendo eadem H E ad H I, atque ad E M eandem proportioner
habebit; & ideo H I ſeu ei æqualis N G æqualis erit E M, quare eadem
L F ad N G, atque ad E M eandem proportionem habebit: ſed propter ſimi-
litudinem triangulorum L C F, M C E eſt F C ad E C, vt F L ad M E,
ſeu ad N G, & erat C E ad E F, necnon D G ad G F in eadem propor-
tione lateris tranſuerſi ad rectum, & ſummæ terminorum ad antece-
44Lem. 1. dentes terminos, ſcilicet F C ad E C, necnon F D ad D G ean-
dem proportionem habent; quare L F ad N G eandem
proportionem habet, quàm F D ad D G, & compa-
rando homologorum differentias L D ad D N
55Lem. 3. eandem proportionem habebit, quàm F D
ad D G, & comparando conſe-
quentes ad differentias termi-
66Lem. 1. norum D N ad L N erit,
vt D G ad F G,
ſcilicet
vt latus tranſuer ſum ad rectum;
quapropter B L eſt linea
779. huius.breuiſsima.

Page concordance

Text layer

Text normalization

Search

Scan	Original
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72

Scan	Original
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72

Scan	Original
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72