## Chauvenet's Treatise on Elementary Geometry |

### From inside the book

Page 189

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**two sides of a triangle proportionally , it is parallel to the third side**. PROPOSITION III . Two triangles are similar when they are mutually equiangular . PROPOSITION IV . Two triangles are similar when an angle in the one is equal to ...### Other editions - View all

### Common terms and phrases

ABCD adjacent angles altitude angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise Find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane angle plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume

### Popular passages

Page 200 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.

Page 133 - The area of a rectangle is equal to the product of its base and altitude.

Page 137 - Two triangles having 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 117 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

Page 214 - The acute angle which a straight line makes with its own projection upon a plane is the least angle which it makes with any line of that plane.

Page 113 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 38 - The sum of the three angles of any triangle is equal to two right angles.

Page 184 - If two triangles have two sides of the 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.

Page 128 - Find the locus of a point the sum of whose distances from two given straight lines is equal to a given constant, k.

Page 52 - 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.