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" If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let... "
The Elements of Euclid, containing the first six books, with a selection of ... - Seite 232
von Euclides - 1874
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 Seiten
...figures upon the sides containing the right angle. PROP. XXXII. THEOREM. If two triangles which have two sides of the one proportional to two sides of...another; the remaining sides shall be in a straight line. PROP. XXXIII. THEOREM. In equal circles, angles, whether at the centres or circumferences, have the...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1849 - 332 Seiten
...PROP. XXXII. THEOR. If two triangles, which have two sides of the one proportional to two sides oj the other, be joined at one angle , so as to have their homologous sides parallel to one another ; their remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have two sides...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 178 Seiten
...Wherefore, in right-angled triangles, ¿c. QED PROPOSITION XXXII. — THEOREM. If tun triangles which liave two sides of the one proportional to two sides of...as to have their homologous sides parallel to one anotlier, the remaining sides shall be in a straight line. LET abС, d С e be two triangles which...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J ..., Bücher 1

Euclides - 1853 - 334 Seiten
...similarly situated with it. Which was to be proved. PEOP. XXXII. THEOE. If two triangles, which have two sides of the one proportional to two sides of the other, be joined at a common angular point so as to have their homologous sides in the proportion parallel : then their...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 Seiten
...demonstration or confirmation of that proposition. PROP. XXXII. THEOREM. If two triangles, which have two sides of the one proportional to two sides of...joined at one angle, so as to have their homologous sities parallel to one another and proceeding from their vertices in the same direction ; the remaining...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 Seiten
...proportional. If two triangles have two sides in the one proportional to two sides in the other, And be joined at one angle so as to have their homologous sides parallel to one another. Or have the angles opposite to one pair of the homologous sides equal; and those opposite to the other...
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The Calendar of King's College, London

1857 - 488 Seiten
...have those angles equal which are opposite to the homologous sides. 10. If two triangles which have two sides of the one proportional to two sides of...; the remaining sides shall be in a straight line. 11. If AB CD be a parallelogram, and P and Q two points in a line parallel to AB, and if PA, QB meet...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 380 Seiten
...Wherefore, in right-angled triangles, &c. QED PROPOSITION XXXII. THEOREM. If two triangles which have two sides of the one proportional to two sides of...remaining sides shall be in a straight line. Let ABC, DCE he two triangles which have the two sides BA, AC proportional to the two CD, DE, viz. BA to AC, as...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 Seiten
...proportional. If two triangles have two sides in the one proportional to two sides in the other, And be joined at one angle so as to have their homologous sides parallel to one another. Or have the angles opposite to one pair of the homologous sides equal ; and those opposite to the other...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 Seiten
...similarly described figures on BA and AC (V. B). PBOPOSITION XXXII. THEOREM. If two triangles, which have two sides of the one proportional to two sides of the other, can be joined at one angle, so as to have their homologous sides parallel to one another, the remaining...
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