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Books Books 1 - 10 of 10 on And the remaining angles of the one coincide with the remaining angles of the other,....
" And the remaining angles of the one coincide with the remaining angles of the other, and are therefore equal to them, namely, the angle ABC to the angle DEF, and the angle ACB to the angle DFE. "
The practice of navigation and nautical astronomy - Page 33
by H. Raper - 1908 - 934 pages
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841
...with the base EF, two straight * 10 AX. lines would enclose a space, which is impossible.* Therefore the base BC coincides with the base EF, and is therefore equal to it. Wherefore the whole triangle ABC coincides with the whole triangle DEF, and is equal to it; and the...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...base EF, the two straight lines BC, EF, would enclose a space, which (Ax. 10) is impossible. Wherefore the base BC coincides with the base EF, and is, therefore, equal (Ax. 8) to it. Wherefore, also, the whole triangle ABC coincides with the whole triangle DEF, and is,...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...the base EF, two straight lines would inclose a space, which is impossible, (ax. 10.) 9. Therefore the base BC coincides with the base EF, and is therefore equal to it. (ax. 8.) 10. Therefore the whole triangle ABC coincides with the whole triangle DEF, and is equal to...
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The practice of navigation and nautical astronomy. [With] Tables [and ...

1870
...sums, and the remaining angles CEA, BED are equal. (No. 112, 4). 117. If two triangles, as ABC, DE F, have two sides of the one, as AB, AC, equal to two...sides being laid on two equal sides) will exactly cover it. Hence the two remaining angles must be equal, or B is equal to E, and C to F; or, the triangles...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...base EF, the two straight lines BC, EF would enclose a space, which is impossible (Ax. 9) wherefore the base BC coincides with the base EF and is, therefore, equal to it. Wherefore, also the whole triangle ABC coincides with the whole triangle DEF, and is, therefore equal...
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The Practice of Navigation and Nautical Astronomy

Henry Raper - Nautical astronomy - 1882 - 910 pages
...sums, and the remaining angles CEA, BED are equal. (No. 112, 4). 1 17. If two triangles, as ABC, DE F, have two sides of the one, as AB, AC, equal to two...sides being laid on two equal sides) will exactly cover it. Hence the two remaining angles must be equal, or B is equal to E, and C to F ; or, the triangles...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1892 - 518 pages
...the base EF; for if not, two straight lines would enclose a space ; which is impossible. Ax. 10. Thus the base BC coincides with the base EF, and is therefore equal to it. Ax. 8. And the triangle ABC coincides with the triangle DEF, and is therefore equal to it in area....
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Mathematics: Mechanic's bids and estimates. Mensuration for beginners. Easy ...

Seymour Eaton - 1899 - 340 pages
...base EF; for, if not, two straight lines would inclose a space, which is impossible (Axiom 4). Thus the base BC coincides with the base EF, and is, therefore, equal to it (Axiom 5). And the triangle ABC coincides with the triangle DEF, and is, therefore, equal to it in...
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A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV.

Henry Sinclair Hall, Frederick Haller Stevens - Geometry - 1900 - 304 pages
...the base EF; for if not, two straight lines would enclose a space ; which is impossible. Ax. 10. Thus the base BC coincides with the base EF, and is therefore equal to it. Ax. 8. And the remaining angles of the triangle ABC coincide with the remaining angles of the triangle...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid, H. S. Hall, F. H. Stevens - Euclid's Elements - 1904 - 456 pages
...the point F. for if not, two straight lines would enclose a space ; which is impossible. Ax. 10. Thus the base BC coincides with the base EF, and is therefore equal to it. Ax. 8. And the remaining angles of the triangle ABC coincide with the remaining angles of the triangle...
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