The Eclectic School Geometry: A Revision of Evan's School GeometryVan Antwerp, Bragg, 1884 - 155 páginas |
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Página 15
... common , they will coincide throughout their mutual extent . 10. Two magnitudes are equal if , when one is ap- plied to the other , they exactly coincide . POSTULATES . 1. A straight line may be drawn in any direction from a point . 2 ...
... common , they will coincide throughout their mutual extent . 10. Two magnitudes are equal if , when one is ap- plied to the other , they exactly coincide . POSTULATES . 1. A straight line may be drawn in any direction from a point . 2 ...
Página 17
... common point . The quantity of the angle is the amount of this divergence . The common point is called the vertex . The lines are the sides of the angle . Thus , BA and BC are the sides , and B the vertex , of the angle ABC ; or , as ...
... common point . The quantity of the angle is the amount of this divergence . The common point is called the vertex . The lines are the sides of the angle . Thus , BA and BC are the sides , and B the vertex , of the angle ABC ; or , as ...
Página 19
... common point is a right angle ( ? ) . THEOREM III . If a straight line intersect two parallels , the correspond- ing inner and outer angles will be equal to each other ; also the alternate angles . Let the straight line EF in- tersect ...
... common point is a right angle ( ? ) . THEOREM III . If a straight line intersect two parallels , the correspond- ing inner and outer angles will be equal to each other ; also the alternate angles . Let the straight line EF in- tersect ...
Página 28
... common , and the angles ACD and BCD are equal by construction . Therefore ( Theo . XII ) the triangles ACD and BCD are equal in all their parts , and the ang . A ang . B. Cor . 1. - CD is perpendicular to AB ( ? ) . Cor . 2. — AD = DB ...
... common , and the angles ACD and BCD are equal by construction . Therefore ( Theo . XII ) the triangles ACD and BCD are equal in all their parts , and the ang . A ang . B. Cor . 1. - CD is perpendicular to AB ( ? ) . Cor . 2. — AD = DB ...
Página 33
... common . B TREOREM XIX . Two triangles which are mutually equilateral are also mutually equiangular . Let the two trian- gles , ABC , DEF , have the three sides AB , BC , CA , respectively equal to the three sides DE , EF , FD . да B ...
... common . B TREOREM XIX . Two triangles which are mutually equilateral are also mutually equiangular . Let the two trian- gles , ABC , DEF , have the three sides AB , BC , CA , respectively equal to the three sides DE , EF , FD . да B ...
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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.