Chauvenet's Treatise on Elementary GeometryJ. B. Lippincott Company, 1887 - 322 páginas |
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Página 55
... radii ; AOC is a diameter . By the definition of a circle , all its radii are equal ; also all its diameters are equal , each being double the radius . If one extremity , O , of a line OA is fixed , while the line revolves in a plane ...
... radii ; AOC is a diameter . By the definition of a circle , all its radii are equal ; also all its diameters are equal , each being double the radius . If one extremity , O , of a line OA is fixed , while the line revolves in a plane ...
Página 56
... radii drawn to its extremities ; as AOB . 3. From the definition of a circle it follows that every point within the circle is at a distance from the centre which is less than the radius ; and every point without the circle is at a ...
... radii drawn to its extremities ; as AOB . 3. From the definition of a circle it follows that every point within the circle is at a distance from the centre which is less than the radius ; and every point without the circle is at a ...
Página 57
... radii , which is con- trary to our hypothesis . PROPOSITION II . - THEOREM . 6. Every diameter bisects the circle and its circumference . Let AMBN be a circle whose centre is O ; then any diameter AOB bisects the circle and its ...
... radii , which is con- trary to our hypothesis . PROPOSITION II . - THEOREM . 6. Every diameter bisects the circle and its circumference . Let AMBN be a circle whose centre is O ; then any diameter AOB bisects the circle and its ...
Página 58
... radii are equal . ( v . Proof of Proposition I. ) 9. COROLLARY . Conversely , in the same circle , or in equal circles , equal arcs subtend equal angles at the centre . 10. Definition . A fourth part of a cir- cumference is called a ...
... radii are equal . ( v . Proof of Proposition I. ) 9. COROLLARY . Conversely , in the same circle , or in equal circles , equal arcs subtend equal angles at the centre . 10. Definition . A fourth part of a cir- cumference is called a ...
Página 59
William Chauvenet, William Elwood Byerly. For , drawing the radii to the extremities of the arcs , the angles O and O ' are equal ( Propo- Α B Α ' B ' sition III . , Corollary ) , and conse- quently the triangles A OB , A'O'B ' , are ...
William Chauvenet, William Elwood Byerly. For , drawing the radii to the extremities of the arcs , the angles O and O ' are equal ( Propo- Α B Α ' B ' sition III . , Corollary ) , and conse- quently the triangles A OB , A'O'B ' , are ...
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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.