Elements of geometry and mensurationLongman, Brown, Green, and Longmans, 1854 - 192 páginas |
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Página 17
... shewn above , that such triangles , applied to each other as in the former case , will coincide in every part , and therefore be equal in all respects * . 25 . PROP . III . To bisect a given angle , that is , to divide it into two equal ...
... shewn above , that such triangles , applied to each other as in the former case , will coincide in every part , and therefore be equal in all respects * . 25 . PROP . III . To bisect a given angle , that is , to divide it into two equal ...
Página 22
... shewn , by bisecting BC in G , joining AG , and proceeding as before , that ACD is greater than ABC . L 33. PROP . XI . The greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC ...
... shewn , by bisecting BC in G , joining AG , and proceeding as before , that ACD is greater than ABC . L 33. PROP . XI . The greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC ...
Página 23
... shewn that they do not meet towards A , C ; .. AB , CD are parallel , according to the Definition of parallel lines ( 12 ) . COR . 1. Produce FE to any point G ; if the exterior angle , as BEG , be equal to the interior and opposite ...
... shewn that they do not meet towards A , C ; .. AB , CD are parallel , according to the Definition of parallel lines ( 12 ) . COR . 1. Produce FE to any point G ; if the exterior angle , as BEG , be equal to the interior and opposite ...
Página 26
... shewn in another very simple way thus : E Let ABC be the triangle , and through C draw DCE parallel to AB ( 36 ) , then the D angles ACB , ACD , BCE are to- gether equal to two right angles ( 30. Cor . 2 ) . But since DE is parallel to ...
... shewn in another very simple way thus : E Let ABC be the triangle , and through C draw DCE parallel to AB ( 36 ) , then the D angles ACB , ACD , BCE are to- gether equal to two right angles ( 30. Cor . 2 ) . But since DE is parallel to ...
Página 28
... shewn that BE = CE ; therefore AD , BC bisect each other in the point E. .. 41. PROP . XIX . All parallelograms , which have one side common and the sides opposite in one and the same straight line , are equal to one another * . Let ...
... shewn that BE = CE ; therefore AD , BC bisect each other in the point E. .. 41. PROP . XIX . All parallelograms , which have one side common and the sides opposite in one and the same straight line , are equal to one another * . Let ...
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Términos y frases comunes
ABCDEF acres base bisect breadth centre chain chord circular circum circumference circumscribing circle compasses construction contained continued fraction curved decimal Diagonal Scale diagram diameter distance divided draw drawn edge equilateral triangle find the area find the length fraction frustum given angle given circle given line given point given straight line given triangle half height Hence hexagon inscribed instrument intersecting join Let ABCD lineal unit magnitude meet multiplied number of equal number of sides number of units opposite angle parallelogram perimeter perpendicular plane surface plot points of division PROB produced PROP proportional Protractor radii radius ratio rectangle rectangular regular polygon represent right angles shew shewn similar similar triangles square feet square foot square inches straight edge subtends suppose trapezium triangle ABC vernier vertex whole yards
Pasajes populares
Página 32 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Página 19 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Página 27 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Página 32 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it; the angle contained by these two sides is a right angle.
Página 43 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Página 17 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Página 22 - Theorem. The greater side of every triangle is opposite to the greater angle. Let ABC be a triangle of which the side AC is greater than the side AB ; the angle ABC is also greater than the angle BCA. Because AC is greater than AB, make...
Página 192 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Página 126 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Página 20 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.