Geometry Without Axioms; Or the First Book of Euclid's Elements. With Alterations and Familiar Notes; and an Intercalary Book in which the Straight Line and Plane are Derived from Properties of the Sphere ...: To which is Added an Appendix ...

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Robert Heward, 1833 - 150 páginas
 

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Página 51 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Página 109 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...
Página 111 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 120 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Página 72 - Any two sides of a triangle are together greater than the third side.
Página 55 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Página 103 - ... twice as many right angles as the figure has sides.
Página 70 - Any two angles of a triangle are together less than two right angles.
Página 138 - ... the exterior angle equal to the interior and opposite on the same side of the line ; and likewise the two interior angles on the same side of the line together equal to two right angles.
Página 106 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.

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