An Elementary Geometry |
From inside the book
Results 1-5 of 10
Page 49
... radii of a cir- A F E G B D cle , or of equal circles , are equal ; also the diameters are equal , and each is equal to double the radius . 5. An Arc is any part of the circumference ; as A FB . 6. A Chord is the straight line joining ...
... radii of a cir- A F E G B D cle , or of equal circles , are equal ; also the diameters are equal , and each is equal to double the radius . 5. An Arc is any part of the circumference ; as A FB . 6. A Chord is the straight line joining ...
Page 52
... radii CA and CB and the chords AE and EB . As equal oblique A lines are equally distant from the perpen- C B E dicular , A D = DB ( I. 52 ) ; and as E is a point in the perpendicular to the middle of A B , it is equally distant from A ...
... radii CA and CB and the chords AE and EB . As equal oblique A lines are equally distant from the perpen- C B E dicular , A D = DB ( I. 52 ) ; and as E is a point in the perpendicular to the middle of A B , it is equally distant from A ...
Page 53
... radii ; therefore the angle AB ( I. 42 ) . But the exterior angle ACD is equal to the sum of the two angles A and B ( I. 39 ) ; therefore the B D angle ACD is equal to half the angle B ; the angle 4 CD is measured by the arc A D ( 14 ) ...
... radii ; therefore the angle AB ( I. 42 ) . But the exterior angle ACD is equal to the sum of the two angles A and B ( I. 39 ) ; therefore the B D angle ACD is equal to half the angle B ; the angle 4 CD is measured by the arc A D ( 14 ) ...
Page 60
... radii of two concentric circles are 40 and 54 feet ; what is the area of the space bounded by their circumferences ? 7. A has a circular lot of land whose diameter is 95 rods , and B a simi- lar lot whose area is 750 square rods ...
... radii of two concentric circles are 40 and 54 feet ; what is the area of the space bounded by their circumferences ? 7. A has a circular lot of land whose diameter is 95 rods , and B a simi- lar lot whose area is 750 square rods ...
Page 62
... radii . 53. Every angle inscribed in a segment greater than a semicircle is acute ; and every angle inscribed in a segment less than a semicir- cle is obtuse . ( 21. ) 54. The angle made by a tangent and a chord is measured by half the ...
... radii . 53. Every angle inscribed in a segment greater than a semicircle is acute ; and every angle inscribed in a segment less than a semicir- cle is obtuse . ( 21. ) 54. The angle made by a tangent and a chord is measured by half the ...
Other editions - View all
Common terms and phrases
A B C ABCD adjacent altitude angle ABC apothem arcs A B base and altitude bisect centre chord circ circumference cone construct the triangle convex surface Corollary cube cylinder diagonals diameter distance divided dodecagon EATON'S equal altitudes equally distant equiangular equilateral feet frustum given angle given circle given line given point given side given square half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining lines A B measured by half number of sides opposite sides parallel planes parallelogram parallelopiped perimeter perpendicular plane parallel quadrilateral radii radius ratio rectangle regular polygon respectively equal rhombus right angles right prism right pyramid right triangle Scholium secant segment similar triangles slant height sphere tangent THEOREM VII trapezoid triangle ABC vertex
Popular passages
Page 25 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 30 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 27 - If the product of two quantities is equal to the product of two others, the...
Page 43 - The area of a regular polygon is equal to half the product of its perimeter and apothem.
Page 11 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 23 - If two triangles have two sides of one respectively equal to two sides of the other, but the third sides unequal...
Page 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.
Page 49 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 70 - A right cylinder is a solid described by the revolution of a rectangle about one of its sides.
Page 64 - DEFINITIONS. 1 . A straight line is perpendicular to a plane, when it is perpendicular to every straight line of the plane which it meets.