The Eclectic School Geometry: A Revision of Evan's School GeometryVan Antwerp, Bragg, 1884 - 155 páginas |
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Página 3
... draw- ing its many figures . It calls into action the reasoning faculty in mastering the demonstrations , and especially in inventing demonstrations and solutions for the theorems and problems which are left for the exercise and ...
... draw- ing its many figures . It calls into action the reasoning faculty in mastering the demonstrations , and especially in inventing demonstrations and solutions for the theorems and problems which are left for the exercise and ...
Página 9
... drawn lines and surfaces of geometry , —the axis of the earth , which the pupil has learned to call imaginary , the equator , the tropics , are as real as the Amazon River , or the great plains of Siberia . The figures which we draw ...
... drawn lines and surfaces of geometry , —the axis of the earth , which the pupil has learned to call imaginary , the equator , the tropics , are as real as the Amazon River , or the great plains of Siberia . The figures which we draw ...
Página 12
... drawn . It is well to notice that not the general theorem , but only one instance , is actually demonstrated ; but that the mode of doing it will apply to every instance which comes under the original conditions . As an illustration ...
... drawn . It is well to notice that not the general theorem , but only one instance , is actually demonstrated ; but that the mode of doing it will apply to every instance which comes under the original conditions . As an illustration ...
Página 13
... drawn between any two points . 9. An hypothesis denotes the supposition made , or the conditions given , in any proposition . Scholium . - In Theorem XI . , just referred to , the condition , that the two straight lines be drawn from ...
... drawn between any two points . 9. An hypothesis denotes the supposition made , or the conditions given , in any proposition . Scholium . - In Theorem XI . , just referred to , the condition , that the two straight lines be drawn from ...
Página 15
... drawn ; and that is the shortest line between them . 9. If two straight lines have two points common , they will coincide throughout their mutual extent . 10. Two magnitudes are equal if , when one is ap- plied to the other , they ...
... drawn ; and that is the shortest line between them . 9. If two straight lines have two points common , they will coincide throughout their mutual extent . 10. Two magnitudes are equal if , when one is ap- plied to the other , they ...
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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.