Elements of Geometry with Notes

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Carey, Lea, & Blanchard, 1833 - 216 من الصفحات
 

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الصفحة 177 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
الصفحة 184 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
الصفحة 31 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
الصفحة 89 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
الصفحة 157 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
الصفحة 24 - The difference of the angles at the base of any triangle, is double the angle contained by a line drawn from the vertex perpendicular to the base, and another bisecting the angle at the vertex.
الصفحة 16 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
الصفحة 213 - We have already said that by the term convex line we understand a line, polygonal, or curve, or partly curve and . partly polygonal, such that a straight line cannot cut it in more than two points.
الصفحة 196 - Now the parallelogram BL is double of the triangle ABD, because they are upon the same base BD, and between the same parallels...
الصفحة 37 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.

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