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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.
The Elements of Euclid: viz. the first six books, together with the eleventh ... - Page 11
by Robert Simson - 1835 - 513 pages

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

Robert Simson - Trigonometry - 1827 - 546 pages
...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, Volume 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828 - 598 pages
...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, Volume 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828 - 598 pages
...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 - Euclid's Elements - 1833 - 168 pages
...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 ...

Euclid - 1835 - 540 pages
...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 Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...one another, the sides which subtend, or are opposite to them, are also equal to one another. VII. Upon the same base, and on the same side of it, there...those which are terminated in the other extremity, equal to one another. VIII. If two triangles have two sides of the one equal two sides of the other,...

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

John Playfair - Euclid's Elements - 1836 - 488 pages
...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...

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

Euclides - Euclid's Elements - 1837 - 112 pages
...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...