## Syllabus of Geometry |

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### Common terms and phrases

acute angle adjacent angles angles are equal base and altitude bases and equal bisecting the angle bisector Calculus centre chord circumference circumscribed decagon Descriptive Geometry diameter dihedral angles directrix ellipse equal altitudes equal angles equal bases equal circles equal respectively equal to one-half equiangular exterior point focal radii frustum Geometry given line given point given polygon given straight line homologous hyperbola hypotenuse included angle interior angles intersection lateral area latus rectum lines are cut lines are parallel Mailing price mean proportional middle points number of sides one-third the product ordinate parabola parallel lines parallelogram parallelopiped perimeter plane parallel plane perpendicular point of contact polygon similar Professor of Mathematics pyramid is equal radius ratio regular inscribed polygon regular polygon right triangle secant segment sides opposite slant height spherical triangle symmetrical with respect tangents drawn tetrahedron THEOREMS third side third straight line triangles are equal triangular prism vertex vertices volume

### Popular passages

Page 8 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 21 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.

Page 9 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.

Page 15 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.

Page 11 - The locus of the middle points of a system of parallel chords is the diameter perpendicular to them.

Page 24 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.

Page 8 - ... is greater than the third side of the second, then the angle opposite the third side of the first triangle is greater than the angle opposite the third side of the second.

Page 15 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.

Page 29 - If from the foot of a perpendicular to a plane a straight line is drawn at right angles to any line in the plane, the line drawn from its intersection with the line in the plane to any point of the perpendicular is perpendicular to the line of the plane. Let AB be a perpendicular to the plane MN, BE a perpendicular from B to any line CD in MN, and EA any line from E to AB.