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" 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 in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity: But this... "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 15
av Euclid - 1810 - 518 sider
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 sider
...other side, in a greater ratio. PROP. 47. Required the locus of the vertices of all equal triangles, upon the same base AB, and upon the same side of it. Let ABC be _,: „ any triangle, upon " the given side of the base, and having the given area, and...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 sider
...upon the same base EF, and upon the same side of it, there can be two triangles 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 imposa 7. 1. sible " ; therefore, if the...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...other side, in a greater ratio. PROP. 47. Required the locus of the vertices of all equal triangles, upon the same base AB, and upon the same side of it. Let ABC be any triangle, upon the given side of the base, and having the given area, and let P be a...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 sider
...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...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,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 471 sider
...on the same side of it, there cannot be two triangles, that have their sides which are terminal ed in one extremity of the base equal to one another,...those which are terminated in the other extremity, equal to one another. Let there be two triangles ACB, ADB, upon the same base AB, and upon the same...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...same base EF, and upon the same side of it, there can be two triangles EDF, 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 (I. 7) ; therefore, if the base...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 sider
...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. 1.) ; therefore, if the...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 sider
...upon the same base EF, and upon the same side of it, there would be two triangles having their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in * Or, if the three aides of one triangle be equal to the three sides of another,...
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The Elements of Euclid

Euclid - 1838 - 416 sider
...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...those which are terminated in the other extremity. QED PROP. VIII. THEOR. IF two triangles have two sides of the one equal to two sides of the other,...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...upon the same base EF, and upon the same side of it, there can be two triangles 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' a- therefore, if the base...
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