The Eclectic School Geometry: A Revision of Evan's School GeometryVan Antwerp, Bragg, 1884 - 155 páginas |
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Página 51
... chord of an arc is the straight line joining its extremities . A а chord produced one way beyond the circumference is called a secant . 5. A segment of a circle is the part contained by an arc and its chord . A sector is the part ...
... chord of an arc is the straight line joining its extremities . A а chord produced one way beyond the circumference is called a secant . 5. A segment of a circle is the part contained by an arc and its chord . A sector is the part ...
Página 53
... chord , drawn perpendicular to a tangent at the point of contact and , terminating in the opposite arc , is a ... chord BC will coincide with the chord AD , and be equal to it . Cor . - Prove the same of equal arcs of equal circles . B ...
... chord , drawn perpendicular to a tangent at the point of contact and , terminating in the opposite arc , is a ... chord BC will coincide with the chord AD , and be equal to it . Cor . - Prove the same of equal arcs of equal circles . B ...
Página 54
... chord , it bisects the chord , and also the arc which the chord subtends . B Let the radius DB be perpen- dicular to the chord AC . It is to be proved that it bisects AC , and also the arc ABC . Draw the radii DA , DC . Now , since the ...
... chord , it bisects the chord , and also the arc which the chord subtends . B Let the radius DB be perpen- dicular to the chord AC . It is to be proved that it bisects AC , and also the arc ABC . Draw the radii DA , DC . Now , since the ...
Página 56
... chord is meas- ured by half the intercepted arc . F E Let AC be a tangent to a circle , and BF a chord drawn from the point of contact B. Then will the angle ABF be measured by half the arc BF , and the angle CBF by half the arc BDF ...
... chord is meas- ured by half the intercepted arc . F E Let AC be a tangent to a circle , and BF a chord drawn from the point of contact B. Then will the angle ABF be measured by half the arc BF , and the angle CBF by half the arc BDF ...
Página 57
... chord , and of two unequal chords the further from the center is the shorter . In the circle C , let ON be any straight line not drawn through the center ; then will any diameter AB be longer than it . Draw radii from the center C to O ...
... chord , and of two unequal chords the further from the center is the shorter . In the circle C , let ON be any straight line not drawn through the center ; then will any diameter AB be longer than it . Draw radii from the center C to O ...
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Términos y frases comunes
allel altitude apothegm Axiom Bisect the angles Book chord circle circumference coincide cone construction convex surface diagonal diameter diedral divided draw drawn equal Theo equal to half equally distant equilateral triangle equivalent exterior angle figure frustum Geometry given angle given line given point given straight line half the product Hence hexagon homologous sides hypotenuse hypothesis inscribed inscribed angle intersection isosceles Let ABC measured by half mutually equiangular number of equal number of sides parallel parallelogram parallelopiped pendicular perimeter perpendicular plane polyedron prism Prove pyramid quadrilateral Ques radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle secant segment slant height sphere square tangent tetraedron THEOREM THEOREM XI third trapezoid trian triangles ABC triedral vertex
Pasajes populares
Página 104 - If from a point without a circle, a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external segment.
Página 32 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Página 54 - The circumference of every circle is supposed to' be divided into 360 equal parts, called degrees ; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.
Página 42 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Página 107 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Página 147 - The areas of two triangles which have 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 140 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Página 50 - The area of a regular polygon is equal to half the product of its apothem and perimeter.
Página 141 - The altitude of a pyramid or cone is the perpendicular distance from the ve~rtex to the base.
Página 39 - The area of a rectangle is equal to the product of its base and altitude.