Pappus Alexandrinus - Mathematical Collection, Book 8

Scan	Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40

1046

η#. Θέσει αἱ ΑΒ ΑΓ, καὶ δοθὲν τὸ Β, καὶ διήχθω ἡ
ΓΔ ἀποτέμνουσα δοθέντα λόγον τὸν τῆς ΑΓ πρὸς ΒΔ·
δεῖξαι ὅτι τοῦ ΑΓΔ τριγώνου τὸ κέντρον τοῦ βάρους ἐστὶ
πρὸς θέσει.

Τετμήσθω ἡ ΑΓ δίχα τῷ Ε, καὶ ἐπιζευχθεῖσα ἡ ΔΕ
τετμήσθω κατὰ τὸ Ζ, ὥστε τὴν ΕΖ τρίτον μέρος εἶναι τῆς

3[Figure 3]ΕΔ· τὸ Ζ ἄρα κέντρον βάρους ἐστὶν
τοῦ ΑΓΔ τριγώνου [1τοῦτο γὰρ προ-
δέδεικται]1. ἤχθω δὴ τῇ ΑΕ παράλ-
ληλος ἡ ΖΗ, καὶ τῆς ΑΒ τρίτον
μέρος ἔστω ἡ ΑΘ. ἔστιν δὲ καὶ
ἡ ΑΗ τρίτον μέρος τῆς ΑΔ, ἐπεὶ
καὶ ἡ ΕΖ τῆς ΕΔ· καὶ λοιπὸν οὖν
ἡ ΘΗ τρίτον μέρος ἐστὶν τῆς ΒΔ.
λόγος δὲ τῆς ΒΔ πρὸς τὴν ΑΓ δο-
θείς [τῆς δὲ ΑΓ πρὸς τὴν ΖΗ·
τριπλασία γὰρ αὐτῆς ἐστιν, ὅτι καὶ
ἡ μὲν ΔΑ τῆς ΔΗ ἡμιολία ἐστίν,
τουτέστιν ἡ ΑΕ τῆς ΖΗ, ἡ δὲ ΓΑ
τῆς ΑΕ διπλῆ]· λόγος ἄρα καὶ τῆς
ΗΘ πρὸς τῆν ΗΖ δοθείς. καὶ δο-
θεῖσα ἡ πρὸς τῷ Η γωνία [1καὶ γὰρ
ἡ πρὸς τῷ Α]1· δοθεῖσα ἄρα καὶ ἡ ὑπὸ ΗΘΖ γωνία. καὶ
δοθὲν τὸ Θ· θέσει ἄρα ἡ ΘΖ εὐθεῖα, καὶ ἔστιν ἐπ' αὐτῆς
τὸ Ζ κέντρον.

Ταῦτα μὲν οὖν καὶ τὰ τοιαῦτα θεωρίαν ἔχει, τὰ δὲ
καὶ εἰς χρείαν δυνάμενα πεσεῖν μηχανικὴν τοιαῦτ' ἂν εἴη.

Page concordance

Text layer

Text normalization

Search

Scan	Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40

Scan	Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40

Scan	Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40