Chauvenet's Treatise on Elementary Geometry |
From inside the book
Results 1-5 of 23
Page 10
... mean the direc- tion in which a point describing the line is moving when it passes through the point in question . Definitions . A straight line is a line which has everywhere the same direction . A curved line is one no portion of ...
... mean the direc- tion in which a point describing the line is moving when it passes through the point in question . Definitions . A straight line is a line which has everywhere the same direction . A curved line is one no portion of ...
Page 71
... means are equal , as in the proportion A : BB : C , the middle term B is called a mean proportional between A and C , and C is called a third proportional to A and B. 37. In cases where it is necessary to prove the equality of ...
... means are equal , as in the proportion A : BB : C , the middle term B is called a mean proportional between A and C , and C is called a third proportional to A and B. 37. In cases where it is necessary to prove the equality of ...
Page 104
William Chauvenet, William Elwood Byerly. a : b Corollary . If the means are equal , as in the proportion b : c , we have b2 ac , whence b Vac ; that is , a mean proportional ( II . , 36 ) between two numbers is equal to the square root ...
William Chauvenet, William Elwood Byerly. a : b Corollary . If the means are equal , as in the proportion b : c , we have b2 ac , whence b Vac ; that is , a mean proportional ( II . , 36 ) between two numbers is equal to the square root ...
Page 105
... means of a proportion , it is implied that at least two of the terms are numbers . If , for example , the terms of the proportion A : B = A ' : B ' are all lines , no meaning can be directly attached to the products A × B ' , B × A ...
... means of a proportion , it is implied that at least two of the terms are numbers . If , for example , the terms of the proportion A : B = A ' : B ' are all lines , no meaning can be directly attached to the products A × B ' , B × A ...
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.