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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

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

John Playfair - 1836 - 311 σελίδες
...two angles, &c. QED COR. Hence every equiangular triangle is also equilateral. ' PROP. VII. THEOR. Upon the same base, and on the same side of it, there...be two triangles, that have their sides which are terminal ed in one extremity of the base equal to one another, and likewise those which are terminated...

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 σελίδες
...Wherefore, if two angles, &c. Cor. Hence every equiangular triangle is also equilateral. 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...

A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 σελίδες
...2. that .'. Aflisnot =/= AC, ie, that AB = AC. PROPOSITION VII. (Argument ad Absurdum.) Theorem. On the same base, and on the same side of it, there cannot be two triangles that have their sides terminated in one extremity of the base equal to each other, and likewise those terminated in the other...

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

John Playfair - 1837 - 318 σελίδες
...then, upon the same base EF, and upon the same side of it, there can be two triangles EOF, EGF,that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity ; but this is impossible (7....

Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...equal to it. COR. — Hence every equiangular triangle is also equilateral. PROPOSITION VII. THEOREM. Upon the same base, and on the same side of it, there cannot he two triangles that have their sides which are terminated in one extremity of the base equal to one...

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 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...are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity. QED PROP. VIII. THEOR....

Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...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. QE n. PROP. VIII. THEOR....

Minutes of the Committee of Council on Education

Great Britain. Committee on Education - 1853
...ability, will suffice for the highest class of certificates. Section 1. 1. Upon the same base and upon the same side of it there cannot be two triangles...terminated in one extremity of the base, equal to one another, and likewise those which are terminated at the other extremity. 2. The greater side of...

The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...them are also equal. COR.—Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. On the same base, and on the same side of it, there cannot be two triangles having their conterminous sides at both extremities of the base, equal to each other. PROP. VIII. THEOR....

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

Euclides - 1840
...— 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 of the base, equal to each...




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