The Eclectic School Geometry: A Revision of Evan's School GeometryVan Antwerp, Bragg, 1884 - 155 páginas |
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Página 23
... joining the same points ( Axiom 8 ) . Therefore the perpendicular BH , which is half of BHB ' , is shorter than BC , which is half of BCB ' ( Axiom 7 ) ; that is , a perpendicular is shorter than an oblique line , if both are drawn to a ...
... joining the same points ( Axiom 8 ) . Therefore the perpendicular BH , which is half of BHB ' , is shorter than BC , which is half of BCB ' ( Axiom 7 ) ; that is , a perpendicular is shorter than an oblique line , if both are drawn to a ...
Página 29
... joining the middle points of the sides of an isosceles triangle to the opposite extremities of the base are equal . ABC is an isosceles triangle , of which AC is the base . By construction , AD = DB and CE EB . Therefore ( Axiom 7 ) ...
... joining the middle points of the sides of an isosceles triangle to the opposite extremities of the base are equal . ABC is an isosceles triangle , of which AC is the base . By construction , AD = DB and CE EB . Therefore ( Axiom 7 ) ...
Página 36
... joins the vertex of a triangle E to the center of the base is less than half the sum of the sides . The line AD , drawn to the center of BC , is prolonged till DE is equal to AD . AC AE BE ( Theo . XII ) . AB + BE . Complete the proof ...
... joins the vertex of a triangle E to the center of the base is less than half the sum of the sides . The line AD , drawn to the center of BC , is prolonged till DE is equal to AD . AC AE BE ( Theo . XII ) . AB + BE . Complete the proof ...
Página 37
... joining two angles not adjacent . Ques . How many diagonals may a quadrilateral have ? A triangle ? 7. The area of any plane figure is the amount of surface which it contains . 8. Two plane figures which will not coincide , but which ...
... joining two angles not adjacent . Ques . How many diagonals may a quadrilateral have ? A triangle ? 7. The area of any plane figure is the amount of surface which it contains . 8. Two plane figures which will not coincide , but which ...
Página 42
... Join FC , BE , and draw BK parallel to AE . Also observe that , since ABC and ABG are right angles , BC and BG form one straight line . Now , in the triangles EAB , CAF , the side EA is equal to the side CA , since they are sides of the ...
... Join FC , BE , and draw BK parallel to AE . Also observe that , since ABC and ABG are right angles , BC and BG form one straight line . Now , in the triangles EAB , CAF , the side EA is equal to the side CA , since they are sides of the ...
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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.