Chauvenet's Treatise on Elementary GeometryJ. B. Lippincott Company, 1887 - 322 páginas |
Dentro del libro
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Página 62
... tangent to each other when they are both tangent to the same straight line at the same point . 21. Definition . A rectilinear figure is said to be circumscribed about a circle when all its sides are tangents to the circumference . In ...
... tangent to each other when they are both tangent to the same straight line at the same point . 21. Definition . A rectilinear figure is said to be circumscribed about a circle when all its sides are tangents to the circumference . In ...
Página 63
... tangent to a circle is perpendicular to the radius drawn to the point of contact . For any other point of the tangent , as D , must lie outside of the circle , and therefore the line OD , joining it with the centre , must be greater ...
... tangent to a circle is perpendicular to the radius drawn to the point of contact . For any other point of the tangent , as D , must lie outside of the circle , and therefore the line OD , joining it with the centre , must be greater ...
Página 64
... tangent , and from any point , P , of the tangent at their point of contact , tangents are drawn to the two circles , the points of contact of these tangents are equally distant from P. PROPOSITION XI . - THEOREM . 27. Two parallels ...
... tangent , and from any point , P , of the tangent at their point of contact , tangents are drawn to the two circles , the points of contact of these tangents are equally distant from P. PROPOSITION XI . - THEOREM . 27. Two parallels ...
Página 65
... tangent , as EF at M , then the intercepted arcs AM and BM are equal . For the radius OM drawn to the point of contact is perpendicular to the tangent ( Proposition IX . ) , and consequently perpendicular also to its parallel AB ...
... tangent , as EF at M , then the intercepted arcs AM and BM are equal . For the radius OM drawn to the point of contact is perpendicular to the tangent ( Proposition IX . ) , and consequently perpendicular also to its parallel AB ...
Página 79
... tangent and a chord is measured by one - half the intercepted arc . Let the angle BAC be formed by the tangent AB and the chord AC ; then it is measured by one - half the intercepted arc AMC . For , draw the diameter AD . The angle BAD ...
... tangent and a chord is measured by one - half the intercepted arc . Let the angle BAC be formed by the tangent AB and the chord AC ; then it is measured by one - half the intercepted arc AMC . For , draw the diameter AD . The angle BAD ...
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.