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Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Five Years in an English University - Σελίδα 348
των Charles Astor Bristed - 1852
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852
...the angle BCA. The sides BA and CA being produced till they meet will be equal.] PROP. VII. THEOR. Upon the same base, and on the same side of it, there...are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity. If it be possible, let...

The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

...in which the vertex of one triangle is upon a side of the other, needs no demonstration. Therefore, upon the same base, and on the same side of it, there...are terminated in one extremity of the base equal to one another, and likewise those which are terminated in, the other extremity, QED PROPOSITION Vin....

The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...angles, &c. QED COB. — Hence every equiangular triangle is also equilateral. PROP. VII. THEOREM. Upon the same base, and on the same side of it, there...are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity. If it be possible, let...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1853 - 317 σελίδες
...in which the vertex of one triangle is upon a side of the other, needs no demonstration. Therefore, upon the same base, and on the same side of it, there...that have their sides which are terminated in one extrem ity of the base equal to one another, and likewise those which are termina ted in the other...

The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 σελίδες
...also equilateral. PROPOSITION VII. — THEOREM. Upon the same lose, and on the same aide of it, tliere cannot be two triangles that have their sides which...are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the otter extremity. IF it be possible, let...

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

Euclides - 1853
...all equal, that is, the triangle ABC is equilateral (Def. 24). Which was to be proved. PEOP. VII. On the same base and on the same side of it there cannot be two triangles which have their sides terminated in one extremity of the base equal, and likewise those terminated...

Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 σελίδες
...is, it is equal to it. Coa. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the same base, and on the same side of it, there cannot be two triangles, that have their sides whieh are terminated in one extremity of the base equal to one another, and likewise those which are...

The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...readier mode of bisecting an angle than that contained in Prop. IX. of this book. PB.OP. VII. THEOREM. Upon the same base, and on the same side of it, there cannot be two triangles having their sides terminated in one extremity of the base, equal to one another, and likewise those...

Manual of Method for the use of teachers in elementary schools

W. F. RICHARDS - 1856 - 184 σελίδες
...i/iis direction is not observed. (Three Hours allowed for this Paper.) EUCLID.— (First Section.) 1. Upon the same base, and on the same side of it,...terminated in one extremity of the base, equal to one another, and likewise those which are terminated in the other extremity. 2. If from the ends of...

Cambridge examination papers: a suppl. to the University calendar, 1856-59

...C. EUCLID (A.) DEFINE a plane rectilineal angle, an acute-angled triangle, a circle, parallel lines. 1. Upon the same base, and on the same side of it,...are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity. 2. Draw a straight line...