Chauvenet's Treatise on Elementary GeometryJ. B. Lippincott Company, 1887 - 322 páginas |
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Página 62
... circumscribed about a circle when all its sides are tangents to the circumference . In the same case , the circle is said to be inscribed in the figure . PROPOSITION VIII . - THEOREM . 22. A straight line 62 ELEMENTS OF GEOMETRY .
... circumscribed about a circle when all its sides are tangents to the circumference . In the same case , the circle is said to be inscribed in the figure . PROPOSITION VIII . - THEOREM . 22. A straight line 62 ELEMENTS OF GEOMETRY .
Página 76
... the other . When the sum of two arcs is a semi - circumference ( that is , 180 ° ) , each is called the supplement of the other . See ( I. , 16 ) . 47. Definitions . An inscribed angle is one whose vertex 76 ELEMENTS OF GEOMETRY .
... the other . When the sum of two arcs is a semi - circumference ( that is , 180 ° ) , each is called the supplement of the other . See ( I. , 16 ) . 47. Definitions . An inscribed angle is one whose vertex 76 ELEMENTS OF GEOMETRY .
Página 77
... inscribed in a segment when its vertex is in the arc of the segment , and its sides pass through the extremities of the subtending chord . Thus , the angle BAC is inscribed in the segment BAC . PROPOSITION XIV . - THEOREM . 48. An ...
... inscribed in a segment when its vertex is in the arc of the segment , and its sides pass through the extremities of the subtending chord . Thus , the angle BAC is inscribed in the segment BAC . PROPOSITION XIV . - THEOREM . 48. An ...
Página 78
... inscribed angle BAC ; then the measure of the angle BAC is one - half of the arc BC . A For , draw the diameter AD . The meas- ure of the angle BAD is , by the first case , one - half the arc BD ; and the measure of the angle CAD is one ...
... inscribed angle BAC ; then the measure of the angle BAC is one - half of the arc BC . A For , draw the diameter AD . The meas- ure of the angle BAD is , by the first case , one - half the arc BD ; and the measure of the angle CAD is one ...
Página 83
... inscribed in a semicircle , is a right angle ( Proposition XIV . , Corollary ) . This construction is often preferable to the preceding , es- pecially when the given point C is at , or near , one extremity of the given line , and it is ...
... inscribed in a semicircle , is a right angle ( Proposition XIV . , Corollary ) . This construction is often preferable to the preceding , es- pecially when the given point C is at , or near , one extremity of the given line , and it is ...
Otras ediciones - Ver todas
Chauvenet's Treatise on Elementary Geometry William Chauvenet,William Elwood Byerly Vista completa - 1887 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 133 - The area of a rectangle is equal to the product of its base and altitude.
Página 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.
Página 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.
Página 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.
Página 113 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Página 38 - The sum of the three angles of any triangle is equal to two right angles.
Página 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.
Página 128 - Find the locus of a point the sum of whose distances from two given straight lines is equal to a given constant, k.
Página 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.