Syllabus of Propositions in Geometry: Intended for Use in Preparing Students for Harvard College and the Lawrence Scientific School |
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Page 13
... REGULAR POLYGONS AND THE MEASURE OF THE CIRCLE . THEOREM I. An equilateral polygon inscribed in a circle is a regular polygon . THEOREM II . A circle may be circumscribed about any regular polygon , and a circle may also be inscribed in ...
... REGULAR POLYGONS AND THE MEASURE OF THE CIRCLE . THEOREM I. An equilateral polygon inscribed in a circle is a regular polygon . THEOREM II . A circle may be circumscribed about any regular polygon , and a circle may also be inscribed in ...
Page 14
... regular polygon inscribed in a circle be increased indefinitely , the apothem of the polygon will approach the radius of the circle as its limit . THEOREM IX . The circumference of a circle is the limit which the perimeters of regular ...
... regular polygon inscribed in a circle be increased indefinitely , the apothem of the polygon will approach the radius of the circle as its limit . THEOREM IX . The circumference of a circle is the limit which the perimeters of regular ...
Page 20
... polygon similar to the base ; 3d , the area of the section is to the area of the base as the square of its distance ... regular pyramid is equal to the product of the perimeter of its base and half its slant height . THEOREM XIII . If ...
... polygon similar to the base ; 3d , the area of the section is to the area of the base as the square of its distance ... regular pyramid is equal to the product of the perimeter of its base and half its slant height . THEOREM XIII . If ...
Page 22
... regular polygon be inscribed in or circumscribed about a given circular cylinder , the volume of the prism will approach the volume of the cylinder as its limit , and the area of its lateral surface will approach the area of the lateral ...
... regular polygon be inscribed in or circumscribed about a given circular cylinder , the volume of the prism will approach the volume of the cylinder as its limit , and the area of its lateral surface will approach the area of the lateral ...
Page 24
... regular polygon , be inscribed in or circumscribed about a given circular cone , the volume of the pyramid will approach the volume of the cone as its limit , and the lateral area of the pyramid will approach the area of the convex ...
... regular polygon , be inscribed in or circumscribed about a given circular cone , the volume of the pyramid will approach the volume of the cone as its limit , and the lateral area of the pyramid will approach the area of the convex ...
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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'.