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" On the same base, and on the same side of it, there cannot be two triangles... "
The school edition. Euclid's Elements of geometry, the first six books, by R ... - Σελίδα 341
των Euclides - 1864
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A treatise on navigation, and nautical astronomy

Edward Riddle - 1824 - 551 σελίδες
...FI) E and ABC are equal, (Cor. Theo. 32.) QED THEOREM XXXVI. If two equal triangles as ABC, AD B, be on the same base AB, and on the same side of it, the line DC which joins their vertices, is parallel to the base A B. For if D С is not parallel to...

Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...B and C are equal. COR. — Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. On the same base (AB), and on the same side of it, there cannot be two triangles having their conterminous sides (AC and AD, BC and BD) at both extremities...

The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 σελίδες
...likewise those which are terminated in the other extremity, equal to one another. If it be possible, upon the same base AB, and on the same side of it, let ACB, ADB be two triangles, which have their sides CA, DA terminated in A, one extremity of the base,...

Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...draw EG perpendicular to DB and meeting DC produced in G. Then CEG is an equilateral triangle. 69. On the same base AB, and on the same side of it, let...angle ABD not a right angle ; then the triangle ABC may be shewn to oe greater than the triangle ABD whether the angle ABD be acute or obtuse. 70. Let...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson with ...

Euclid, Robert Potts - 1847 - 478 σελίδες
...draw EG perpendicular to DB and meeting DC produced in G. Then CEG is an equilateral triangle. 69. On the same base AB, and on the same side of it, let...angle ABD not a right angle; then the triangle ABC may be shewn to oe greater than the triangle ABD whether the angle ABD be acute or obtuse. 70. Let...

The Elements of Euclid [book 1] for beginners, by J. Lowres

Euclides - 1852
...those sides which terminate in the other end of the base are not equal. Let the triangles ACB and ADB, on the same base AB, and on the same side of it, have the sides AC and AD equal; then the sides вc and BD are not equal. CASE 1. When the vertex of...

The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J ..., Βιβλίο 1

Euclides - 1853
...BD by hyp8 : which is impossible. Hence in every case it has been shewn impossible for there to be on the same base AB, and on the same side of it, two triangles ACB, ADB, having their sides AC, AD terminated in one extremity A of the base equal,...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 σελίδες
...ways, and the figure may be transformed into a triangle, by two constructions similar to that employetl for a figure of four sides. If the figure consists...be a triangle whose vertical angle is A, and whose base BC is bisected in D ; let any line EDG be drawn through D, meeting AC the greater side in G and...

Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864
...bisection of the base parallel to the two sides of the triangle. 108. This may be shewn ex absurdo. 1 09. On the same base AB, and on the same side of it, let...constructed, having the side BD equal to BC, the angle ABC aright angle, but the angle ABD not a right angle; then the triangle ABC is greater than ABD, whether...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 σελίδες
...to one another, and likewise those which are terminated at the other extremity. If it be possible, on the same base AB, and on the same side of it, let there be two triangles ACB, £ B ADB, having their sides CA, DA, which are terminated at the extremity...




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