Elements of Geometry and Mensuration: With Easy Exercises, Designed for Schools and Adult ClassesLongman, 1859 - 362 páginas |
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Página 15
... Shew that , if the angles at the base of a triangle are equal to one another , the triangle is isosceles " . ( 7 ) ' reductio ad absurdum ' , ( reducing to an absurdity ) , is a particular mode of demonstration often used by Euclid . It ...
... Shew that , if the angles at the base of a triangle are equal to one another , the triangle is isosceles " . ( 7 ) ' reductio ad absurdum ' , ( reducing to an absurdity ) , is a particular mode of demonstration often used by Euclid . It ...
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 . 2 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 . 2 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 ...
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Términos y frases comunes
ABCDEF angular points base bisect centre chain chord circular circumference circumscribed circumscribing circle compasses cone construction cubic curved cylinder describe a circle diagonal diameter distance divided draw a straight drawn edge equal angles equal arcs equilateral triangle feet find the area foot frustum given angle given circle given line given point given ratio given straight line given triangle greater height Hence hexagon inches inscribed instrument intersecting length Let ABCD magnitude measure meet number of sides opposite angle parallelogram parallelopiped perimeter perpendicular plane surface points of division prism PROB produced PROP proportional Protractor radii radius rectangle rectangle contained regular polygon right angles ruler scale segment semi-circle shew shewn similar triangles square of AB square of AC subtends suppose tangent trapezium triangle ABC unit 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 16 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle, shall be greater than the base of the other.
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 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 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 223 - 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 128 - 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.