The Eclectic School Geometry: A Revision of Evan's School GeometryVan Antwerp, Bragg, 1884 - 155 páginas |
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Página 37
... equivalent . Ques . When are two plane figures equal ? ( Ax . 10. ) THEOREM XX . The opposite sides and angles of a parallelogram are equal to each other . The figure ABCD is a parallelo- gram . Draw the diagonal AC . How many pairs of ...
... equivalent . Ques . When are two plane figures equal ? ( Ax . 10. ) THEOREM XX . The opposite sides and angles of a parallelogram are equal to each other . The figure ABCD is a parallelo- gram . Draw the diagonal AC . How many pairs of ...
Página 41
... equivalent to ABCD . Since AB and DC are opposite sides of a parallelo- gram , they are equal ( Theo . XX ) ; and , for the same reason , AB and EF are equal ; therefore , DC is equal to EF ( Ax . 1 ) . Taking away each of these in turn ...
... equivalent to ABCD . Since AB and DC are opposite sides of a parallelo- gram , they are equal ( Theo . XX ) ; and , for the same reason , AB and EF are equal ; therefore , DC is equal to EF ( Ax . 1 ) . Taking away each of these in turn ...
Página 42
... equivalent to the sum of the squares described on the other two sides . A B E K H Let ABC be a triangle right- angled at B. It is to be proved that the square AEDC is equiva- lent to the sum of the squares ABGF and BHIC . Join FC , BE ...
... equivalent to the sum of the squares described on the other two sides . A B E K H Let ABC be a triangle right- angled at B. It is to be proved that the square AEDC is equiva- lent to the sum of the squares ABGF and BHIC . Join FC , BE ...
Página 43
... equivalent to the square BAFG . In the same manner ( by joining AI and BD ) , it may be shown that the parallelogram CDKL is equivalent to the square BCIH . Hence , the whole square ACDE is equivalent to the sum of the squares BAFG ...
... equivalent to the square BAFG . In the same manner ( by joining AI and BD ) , it may be shown that the parallelogram CDKL is equivalent to the square BCIH . Hence , the whole square ACDE is equivalent to the sum of the squares BAFG ...
Página 52
... equivalent to the arc ADC , and the segment ABC to the segment ADC ( Ax . 10 ) . Therefore , a diameter divides , etc. THEOREM XXX If a straight line is perpendicular to a diameter at its extremity , it is a tangent to the circle ...
... equivalent to the arc ADC , and the segment ABC to the segment ADC ( Ax . 10 ) . Therefore , a diameter divides , etc. THEOREM XXX If a straight line is perpendicular to a diameter at its extremity , it is a tangent to the circle ...
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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.