The Elements of Plane and Solid Geometry: With Numerous ExercisesD.C. Heath & Company, 1890 - 393 σελίδες |
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Αποτελέσματα 1 - 5 από τα 66.
Σελίδα 17
... intersect each other , the four angles which they make at the point of intersection , are together equal to four right angles . If one of the four angles is a right angle , the other three are right angles , and the lines are mutually ...
... intersect each other , the four angles which they make at the point of intersection , are together equal to four right angles . If one of the four angles is a right angle , the other three are right angles , and the lines are mutually ...
Σελίδα 31
... intersect in G. B M H A Then since the s AB and DE are cut by BC , .. Z ABC = < DGC . And since the s BC and MF are cut by DH , .. DGC = < DEF . .. Z ABC = < DEF . / DEF is the supplement of DEM . F ( 177 ) ( 177 ) ( Ax . 1 ) ( 25 ) ...
... intersect in G. B M H A Then since the s AB and DE are cut by BC , .. Z ABC = < DGC . And since the s BC and MF are cut by DH , .. DGC = < DEF . .. Z ABC = < DEF . / DEF is the supplement of DEM . F ( 177 ) ( 177 ) ( Ax . 1 ) ( 25 ) ...
Σελίδα 37
... intersection F. ... the two As coincide in all their parts , and are equal . Q.E.D. 106. COR . 1. Two right - angled triangles are equal when the hypotenuse and an acute angle of the one are equal respectively to the hypotenuse and an ...
... intersection F. ... the two As coincide in all their parts , and are equal . Q.E.D. 106. COR . 1. Two right - angled triangles are equal when the hypotenuse and an acute angle of the one are equal respectively to the hypotenuse and an ...
Σελίδα 50
... intersect at O. To prove AO OC , DO = OB . = Proof . In the As AOB , COD , A B AB = DC , being opp . sides of the ( 129 ) , and ZABO CDO , = 2BAO = _DCO , being alt . - int . Ls ( 72 ) . ΔΑΟΒ = A COD , having a side and the two adj . Ls ...
... intersect at O. To prove AO OC , DO = OB . = Proof . In the As AOB , COD , A B AB = DC , being opp . sides of the ( 129 ) , and ZABO CDO , = 2BAO = _DCO , being alt . - int . Ls ( 72 ) . ΔΑΟΒ = A COD , having a side and the two adj . Ls ...
Σελίδα 51
... intersection C ' . .. the two Os coincide throughout , and are equal . Q. E. D. 136. COR . Two rectangles are equal when they have two adjacent sides equal , each to each . POLYGONS . 137. A polygon is a plane figure bounded BOOK I ...
... intersection C ' . .. the two Os coincide throughout , and are equal . Q. E. D. 136. COR . Two rectangles are equal when they have two adjacent sides equal , each to each . POLYGONS . 137. A polygon is a plane figure bounded BOOK I ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude angles are equal base bisect bisector called centre chord circumference circumscribed coincide common cone of revolution Cons construct cylinder diagonals diameter diedral angle distance divided draw equally distant equivalent EXERCISES exterior angle faces feet Find the area Find the volume frustum given circle given line given point given straight line homologous homologous sides hypotenuse inches intersection isosceles triangle lateral area lateral edges Let ABC meet middle point number of sides parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced Proposition Proposition 13 pyramid quadrilateral radii radius ratio rectangle rectangular parallelopiped regular inscribed regular polygon right angles segment similar slant height sphere spherical polygon spherical triangle square surface symmetrical tangent tetraedron Theorem triangle ABC triangular prism triedral vertex
Δημοφιλή αποσπάσματα
Σελίδα 74 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Σελίδα 188 - Two triangles having 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.
Σελίδα 45 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Σελίδα 137 - Terms of the proportion. The first and fourth terms are called the Extremes, and the second and third the Means.
Σελίδα 12 - AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums will be equal.
Σελίδα 206 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Σελίδα 97 - BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by half of the arc BOC, less than a semicircumference.
Σελίδα 334 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Σελίδα 12 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 253 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.