Syllabus of Propositions in Geometry: Intended for Use in Preparing Students for Harvard College and the Lawrence Scientific School |
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Page 10
... perimeters of two similar polygons are in the same ratio as any two corresponding sides . THEOREM VIII . If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The two triangles thus ...
... perimeters of two similar polygons are in the same ratio as any two corresponding sides . THEOREM VIII . If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The two triangles thus ...
Page 12
... perimeters . THEOREM VIII . The square described on the hypotenuse of a right triangle is equivalent to the sum of the squares described on the other two sides . BOOK V. REGULAR POLYGONS AND THE MEASURE OF THE CIRCLE 12.
... perimeters . THEOREM VIII . The square described on the hypotenuse of a right triangle is equivalent to the sum of the squares described on the other two sides . BOOK V. REGULAR POLYGONS AND THE MEASURE OF THE CIRCLE 12.
Page 13
... perimeters of regular polygons of the same number of sides are to each other as the radii of the circumscribed circles , or as the radii of the inscribed circles ; and their areas are to each other as the squares of these radii ...
... perimeters of regular polygons of the same number of sides are to each other as the radii of the circumscribed circles , or as the radii of the inscribed circles ; and their areas are to each other as the squares of these radii ...
Page 14
... perimeter of any polygon circumscribed about it ; it being assumed that the length of an arc of a circle is less ... perimeters of regular inscribed and circumscribed polygons approach when the number of their sides is increased ...
... perimeter of any polygon circumscribed about it ; it being assumed that the length of an arc of a circle is less ... perimeters of regular inscribed and circumscribed polygons approach when the number of their sides is increased ...
Page 19
... perimeter of a right section of the prism and of a lateral edge . Corollary . The lateral area of a right prism is equal to the product of the perimeter of its base and of its altitude . THEOREM II . Two prisms are equal , if three ...
... perimeter of a right section of the prism and of a lateral edge . Corollary . The lateral area of a right prism is equal to the product of the perimeter of its base and of its altitude . THEOREM II . Two prisms are equal , if three ...
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Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ... Harvard University No preview available - 2015 |
Common terms and phrases
adjacent angles angle formed angles are equal apothem bases and equal bisect bisector BOOK centre circle is equal circular cone circular cylinder circumscribed Corollary Corollary II cubes diameter dicular diedral angles equal altitudes equal bases equal circles equal or sym equally distant given point given straight line hypotenuse included angle intercepted arc interior angles lateral area line a plane line is perpendicular lines are cut lines are parallel mean proportional number of sides opposite angles parallel lines parallelogram passed parallel perpen Plane Geometry plane passing plane perpendicular point of contact prism is equal propositions pyramid is divided pyramid is equal quadrilateral radii radius rectangle rectangular parallelopiped regular polygon respectively equal right angles right triangle secant line segment shortest line slant height Solid Geometry sphere are equal spherical triangle squares straight line drawn surface Syllabus THEOREM VII THEOREM VIII third straight line triangles are equal triangular prism triangular pyramid VIII
Popular passages
Page 26 - The angle of two arcs of great circles is equal to the angle of their planes, and is measured by the arc of a great circle described from its vertex as a pole and included between its sides (produced if necessary).
Page 12 - Prove that the square described on the hypotenuse of a right triangle is equivalent to the sum of the squares described on the other two sides.
Page 10 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 7 - In the same circle, or in equal circles, equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Page 4 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.
Page 2 - If two triangles have two sides of one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side. If two triangles have two sides of...
Page 19 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. OM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =0= GM' . Proof. The lateral edges of GM
Page 5 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page 9 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 20 - The volume of a triangular prism is equal to the product of its base by its altitude. A~ Let V denote the volume, B the base, and H the altitude of the triangular prism CEA-E'.