Elements of Geometry: With, Practical ApplicationsD. Appleton and Company, 1850 - 320 σελίδες |
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Αποτελέσματα 6 - 10 από τα 24.
Σελίδα 102
... divided into proportional parts . Let DF be parallel to the side BC of the triangle ABC ; then will AD : DB :: AF : FC . For , draw BF and CD ; then , the triangles DBF , FCD are equal to each other , be- B D F cause they have the same ...
... divided into proportional parts . Let DF be parallel to the side BC of the triangle ABC ; then will AD : DB :: AF : FC . For , draw BF and CD ; then , the triangles DBF , FCD are equal to each other , be- B D F cause they have the same ...
Σελίδα 104
... divided ; in the present case , four times . Join GB , and draw CH , DK , FL parallel to GB ; and then will the line be divided at the points H , K , L , as required . For , by reason of parallels , we have ( B. IV , Prop . v , ) AC ...
... divided ; in the present case , four times . Join GB , and draw CH , DK , FL parallel to GB ; and then will the line be divided at the points H , K , L , as required . For , by reason of parallels , we have ( B. IV , Prop . v , ) AC ...
Σελίδα 113
... divided proportionally , D K H G each being halved , the line FG must be parallel to AC , ( B , IV , Prop . vi . ) In the same way we may show that HK is parallel to AC , and therefore FG and HK are parallel . Furthermore we shall have ...
... divided proportionally , D K H G each being halved , the line FG must be parallel to AC , ( B , IV , Prop . vi . ) In the same way we may show that HK is parallel to AC , and therefore FG and HK are parallel . Furthermore we shall have ...
Σελίδα 130
... divided at the point G , so that the rectangle of the two parts is equal to the square C. - Schol . When the side of the given square is greater than half the given line AB , the line DF , drawn as above directed , will not cut the ...
... divided at the point G , so that the rectangle of the two parts is equal to the square C. - Schol . When the side of the given square is greater than half the given line AB , the line DF , drawn as above directed , will not cut the ...
Σελίδα 137
... divided at the point G in the manner required ; that is , we shall have AB : AG :: AG : GB . :: For , AB being perpendicular to the radius CB at its extremity B , is a tangent , and AF is a secant ; hence we have AF AB AB AD ; [ B. IV ...
... divided at the point G in the manner required ; that is , we shall have AB : AG :: AG : GB . :: For , AB being perpendicular to the radius CB at its extremity B , is a tangent , and AF is a secant ; hence we have AF AB AB AD ; [ B. IV ...
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Elements of Geometry With Practical Applications George R Perkins Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a+b+c altitude angle ABC angle BAC angle BCD bisect centre chord circ circular sector circumference circumscribed polygon coincide cone consequently convex surface cylinder denote diagonal diameter dicular distance draw equal and parallel equiangular equilateral triangle equivalent exterior angle figure formed given line greater half the arc hypothenuse inscribed circle intersection isosceles join less Let ABC line AC line CD lines drawn measured by half meet multiplied number of sides parallel planes parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN point G prism PROBLEM produced Prop PROPOSITION pyramid radii radius rectangle regular polygon respectively equal right-angled triangle Sabc Schol Scholium scribed semicircle semicircumference side AC similar similar triangles solid angle sphere spherical triangle square straight line suppose tangent THEOREM three sides triangle ABC triangular prism vertex VIII
Δημοφιλή αποσπάσματα
Σελίδα 231 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Σελίδα 147 - PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle : it is required to inscribe a circle in the triangle ABC.
Σελίδα 17 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Σελίδα 28 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Σελίδα 233 - The volume of a cylinder is equal to the product of its base by its altitude. Let the volume of the cylinder be denoted by V, its base by B, and its altitude by H.
Σελίδα 276 - THEOREM. Two triangles on the same sphere, or on equal spheres, are equal in all their parts, when they have each an equal angle included between equal sides. Suppose the side...
Σελίδα 120 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 18 - If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another.
Σελίδα 232 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Σελίδα 96 - Similar figures, are those that have all the angles of the one equal to all the angles of the other, each to each, and the sides about the equal angles proportional.