The Eclectic School Geometry: A Revision of Evan's School GeometryVan Antwerp, Bragg, 1884 - 155 páginas |
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Página 9
... edges of the cube . If the line should shorten till the eye can detect no length , the result would be a point . The epithet imaginary is used as definitive of geo- metric lines , denoting that they are visible only to the imagining ...
... edges of the cube . If the line should shorten till the eye can detect no length , the result would be a point . The epithet imaginary is used as definitive of geo- metric lines , denoting that they are visible only to the imagining ...
Página 14
... edge is the result of inference . Intuitive or self - evident truths are called axioms.- ( Sec . II . , Def . 1. ) Some of them lie at the base of mathematics in gen- eral ; others relate specially to magnitudes in space , and are ...
... edge is the result of inference . Intuitive or self - evident truths are called axioms.- ( Sec . II . , Def . 1. ) Some of them lie at the base of mathematics in gen- eral ; others relate specially to magnitudes in space , and are ...
Página 129
... edges are AB and EF , and those whose edges are AD and EG , may be proved equal . Ques.- Will the equality of the plane angles OVS and NPX prove the equality of the diedrals B - AD - C and F - EG - H ? Sch . - Notice that the ...
... edges are AB and EF , and those whose edges are AD and EG , may be proved equal . Ques.- Will the equality of the plane angles OVS and NPX prove the equality of the diedrals B - AD - C and F - EG - H ? Sch . - Notice that the ...
Página 132
... edges are perpendicular to the faces . Any other parallelopiped is called oblique . When the bases are rectangles , the figure is a rectangular parallelopiped . 9. A cube is a right parallelopiped whose length , breadth , and height are ...
... edges are perpendicular to the faces . Any other parallelopiped is called oblique . When the bases are rectangles , the figure is a rectangular parallelopiped . 9. A cube is a right parallelopiped whose length , breadth , and height are ...
Página 134
... edges AF and BG - since , by definition , they are both per- pendicular to the face DB - must be perpendicular also to the straight line AB , which they meet in that plane ( Def . 3 , Sec . XIV ) . Hence , ABGF , or any face of a right ...
... edges AF and BG - since , by definition , they are both per- pendicular to the face DB - must be perpendicular also to the straight line AB , which they meet in that plane ( Def . 3 , Sec . XIV ) . Hence , ABGF , or any face of a right ...
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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.