Elementary GeometryJ.B. Lippincott Company, 1893 |
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Page 71
... 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 incommensurable ratios , it is usually best to employ what is called the method of limits ...
... 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 incommensurable ratios , it is usually best to employ what is called the method of limits ...
Page 104
William Chauvenet. = Corollary . If the means are equal , as in the proportion a : b = b : c , we have bac , whence b Vac ; that is , a mean proportional ( II . , 36 ) between two numbers is equal to the square root of their product . 6 ...
William Chauvenet. = Corollary . If the means are equal , as in the proportion a : b = b : c , we have bac , whence b Vac ; that is , a mean proportional ( II . , 36 ) between two numbers is equal to the square root of their product . 6 ...
Page 116
... mean proportional between the seg- ments of the hypotenuse ; 3d . Each side about the right angle is a mean proportional between the hypotenuse and the adjacent segment . Let C be the right angle of the triangle ABC , and CD the ...
... mean proportional between the seg- ments of the hypotenuse ; 3d . Each side about the right angle is a mean proportional between the hypotenuse and the adjacent segment . Let C be the right angle of the triangle ABC , and CD the ...
Page 117
... mean proportional between the segments of the diam- eter . Suggestion . Draw the chords AC and CB . ( v . II . , Proposition XIV . , Corollary . ) A D B PROPOSITION X. - THEOREM . 28. The square of the length of the hypotenuse of a ...
... mean proportional between the segments of the diam- eter . Suggestion . Draw the chords AC and CB . ( v . II . , Proposition XIV . , Corollary . ) A D B PROPOSITION X. - THEOREM . 28. The square of the length of the hypotenuse of a ...
Page 120
... mean proportional between the segments of any other chord drawn through that point . ( v . II . , 19 , Exercise . ) PROPOSITION XII . - THEOREM . Д B 34. If two secants intersect without a circle , the whole secants and their external ...
... mean proportional between the segments of any other chord drawn through that point . ( v . II . , 19 , Exercise . ) PROPOSITION XII . - THEOREM . Д B 34. If two secants intersect without a circle , the whole secants and their external ...
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Common terms and phrases
ABCD adjacent angles altitude angle BAC 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 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 127 - The area of a rectangle is equal to the product of its base and altitude.
Page 196 - 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 131 - 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 245 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Page 278 - A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let...
Page 111 - 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 48 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Page 57 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 34 - The sum of the three angles of any triangle is equal to two right angles.