New Elementary Geometry: With Practical Applications : a Shorter Course Upon the Basis of the Larger WorkRobert S. Davis & Company, 1874 - 176 páginas |
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Página 12
... coincide throughout their whole ex- tent , are equal . POSTULATES . 27. A Postulate is a self - evident problem ; such as , — 1. That a straight line may be drawn from one point to another . 2. That a straight line may be produced to ...
... coincide throughout their whole ex- tent , are equal . POSTULATES . 27. A Postulate is a self - evident problem ; such as , — 1. That a straight line may be drawn from one point to another . 2. That a straight line may be produced to ...
Página 16
... coincide with the third side EF ( 26 , Ax . 10 ) . Hence the triangle A B C coincides with triangle D E F , and they are therefore equal ( 26 , Ax . 12 ) . 43. Cor . When , in two triangles , these three parts are equal , namely , the ...
... coincide with the third side EF ( 26 , Ax . 10 ) . Hence the triangle A B C coincides with triangle D E F , and they are therefore equal ( 26 , Ax . 12 ) . 43. Cor . When , in two triangles , these three parts are equal , namely , the ...
Página 17
... coincide with each . other , and are therefore equal ( 26 , Ax . 12 ) . 45. Cor . When , in two triangles , these three parts are equal , namely , the angle B equal to the angle E , the angle C equal to the angle F , and the side BC ...
... coincide with each . other , and are therefore equal ( 26 , Ax . 12 ) . 45. Cor . When , in two triangles , these three parts are equal , namely , the angle B equal to the angle E , the angle C equal to the angle F , and the side BC ...
Página 47
... coincide with the curve line E G F ( Theo . I. ) . But , by hypothesis , the arc A D is equal to the arc E G ; hence the point D will fall on G ; hence the chord AD is equal to the chord E G ( 26 , Ax . 10 ) . Conversely , if the chord ...
... coincide with the curve line E G F ( Theo . I. ) . But , by hypothesis , the arc A D is equal to the arc E G ; hence the point D will fall on G ; hence the chord AD is equal to the chord E G ( 26 , Ax . 10 ) . Conversely , if the chord ...
Página 48
... coincide with each other ; hence they must be equal ( 26 , Ax . 12 ) . THEOREM III . 142. In the same circle , or in equal circles , a greater arc is subtended by a greater chord ; and , conversely , the greater chord subtends the ...
... coincide with each other ; hence they must be equal ( 26 , Ax . 12 ) . THEOREM III . 142. In the same circle , or in equal circles , a greater arc is subtended by a greater chord ; and , conversely , the greater chord subtends the ...
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New Elementary Geometry with Practical Applications Benjamin Greenleaf Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD ABCDEF alti altitude Theo angle A CD axis base multiplied bisect chord circum circumference circumscribed cone convex surface D E F diagonal diameter divided ELEMENTARY ALGEBRA ellipse entire surface equal Theo equivalent formed frustum greater GREENLEAF'S half the sum hence homologous homologous sides hypothenuse inches inscribed circle inscribed square intersection magnitudes mean proportional measured by half Metric System number of sides parallelogram parallelopipedon perimeter perpendicular prism PROBLEM quadrilateral radii radius ratio rectangle rectangular regular polygon Required the area Required the volume rhombus right angles Theo right pyramid rods Scholium SCHOOLS sector semicircle side A B side B C similar slant hight solid sphere is equal spherical square described square feet square root tangent THEOREM third triangles A B C triangular triangular prism tude vertex
Pasajes populares
Página 23 - 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 83 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar.
Página 29 - 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.
Página 61 - At a point in a given straight line to make an angle equal to a given angle.
Página 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Página 93 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Página 62 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Página 100 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...
Página 88 - FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.
Página 124 - But the solidity of each triangular prism is equal to the product of its base by its altitude ; and.