## Syllabus of Propositions in Geometry: Intended for Use in Preparing Students for Harvard College and the Lawrence Scientific School |

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Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ... Harvard University No preview available - 2015 |

Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ... Harvard University No preview available - 2016 |

### Common terms and phrases

adjacent angles altitude angles are equal approach arcs axis base bisect bisector BOOK centre chord circular cone circular cylinder circumference circumscribed construct Conversely Corollary Corollary II cubes described diameter dicular diedral angles division draw drawn edge equal altitudes equal circles equally distant equivalent extremities face angles four given point given straight line greater half hypotenuse included angle increased indefinitely inscribed interior angles intersection lateral area length less limit line is perpendicular lines are cut lines are parallel lying measured meet number of sides opposite parallel lines parallelogram perimeter plane passing plane perpendicular point of contact pole prism prism is equal propositions pyramid quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right triangle secant segment similar Solid Geometry sphere spherical triangle squares straight line drawn surface Syllabus tangent teacher THEOREM VII THEOREM VIII third triangles are equal triedral VIII volume

### 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'.