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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

Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Euclid, Rev. John Allen - 1822 - 494 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 - 372 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...

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

Robert Simson - 1827 - 513 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
...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,...are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.' Now we presume there...

The North American Review, Τόμος 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828
...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,...are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.' Now we presume there...

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

Thomas Perronet Thompson - 1833 - 150 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
...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 - 513 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....

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

Robert Simson - 1835 - 513 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,...

The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 σελίδες
...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...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....




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