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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, equal to one another. "
Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ... - Σελίδα 8
των Stewart W. and co - 1884
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - 1822 - 508 σελίδες
...it are equal, and therefore the sides opposite to them. PROP. VII. THEOR. Upon the same base (AB), and on the same side of it, there cannot be two triangles (ACB, ADB), whose conterminous sides are equal, (namely AC to AD, and BC to BD). For, if possible,...

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 1046 σελίδες
...in which the vertex of one triangle is upon a side of the other, needs uo demonstration. Therefore, upon the same base, and on the same side of it, there...triangles, that have their sides which are terminated >n one extremity of the base equal to one another, and likewise those which are terminated in the other...

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

John Playfair - 1826 - 326 σελίδες
...the same base, and on the same side of it, thereeasnot be two triangles that have their sides whieh are terminated in one extremity of the base equal to one another, and likewise those whieh are terminated iu the other extremity equal to one another, QED ~f PROP. VIII. THEOR. If two...

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

Robert Simson - 1827 - 546 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 can- See N. not be two triangles that have their sides which are terminated in one extremity of the...

The North American Review, Τόμος 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 σελίδες
...angles, the lines AI, BD, produced, will meet.' The other is from Simson's Euclid, prop. 7, b. 1 . ' Upon the same base and on the same side of it, there...those which are terminated in the other extremity.' Now we presume there can be no doubt, which of these two methods is best adapted to the conception...

The North American Review, Τόμος 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 σελίδες
...right angles, the lines AI, BD, produced, will meet.' The other is from Simson's Euclid, prop. 7, b. 1. 'Upon the same base and on the same side of it, there...those which are terminated in the other extremity.' Now we presume there can be no doubt, which of these two methods is best adapted to the conception...

Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 168 σελίδες
...CA, AB are all equal to one another. PROPOSITION VII. THEOREM. — Upon the same given straight line and on the same side of it, there cannot be two triangles...their sides which are terminated in one extremity of it equal to one another, and also those which are terminated in the other See Note. extremity. For...

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

Euclides - 1834 - 518 σελίδες
...triangle is also equilateral. PROPOSITION VII. See N. THEOR. — Upon the same base, and on the mine side of it, there cannot be two triangles that have their sides which arc terminated in one extremity of the base, equal to one a not her, and likewise those which are terminated...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 σελίδες
...different situation as EG, FG : then, upon the same base EF, and upon the same side of it, there can be two triangles that have their sides which are terminated...extremity of the base equal to one another, and likewise their sides terminated in the other extremity : But this is imposa 7. 1. sible " ; therefore, if the...

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

Robert Simson - 1835 - 544 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 cannot be two trianyles that have tfieir sides which are terminated in one extremity of the base equal to one another,...




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