Elements of Geometry: With, Practical ApplicationsD. Appleton and Company, 1850 - 320 σελίδες |
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Αποτελέσματα 6 - 10 από τα 38.
Σελίδα 74
... intersection of the diagonals . F A A B B Let lines be drawn from the point P to the corners of the paral- lelogram ABCD , and to the intersection F of the diagonals . Then , from the triangle PDB , we have , ( B. II , Prop . XII ...
... intersection of the diagonals . F A A B B Let lines be drawn from the point P to the corners of the paral- lelogram ABCD , and to the intersection F of the diagonals . Then , from the triangle PDB , we have , ( B. II , Prop . XII ...
Σελίδα 79
... centre . Draw any two chords AB , BC ; bi- sect them with the perpendiculars DF and GH ; then will the point K , in which they intersect , be the centre sought . A H For , by the corollary of the preceding proposition , BOOK III . 79.
... centre . Draw any two chords AB , BC ; bi- sect them with the perpendiculars DF and GH ; then will the point K , in which they intersect , be the centre sought . A H For , by the corollary of the preceding proposition , BOOK III . 79.
Σελίδα 89
... intersection of two chords , is measured by half the sum of the two intercepted arcs . Let the two chords AB , CD inter- sect at the point F ; then will the angle AFC , or its equal BFD , be measured by half the sum of the arcs AC and ...
... intersection of two chords , is measured by half the sum of the two intercepted arcs . Let the two chords AB , CD inter- sect at the point F ; then will the angle AFC , or its equal BFD , be measured by half the sum of the arcs AC and ...
Σελίδα 124
... intersection of DE and IH , it is evi- dent , because of the parallel lines , that the three triangles PHM , PFE and MDI are equiangular . Therefore , all equiangular tri- angles being in the ratio of the squares of their homologous ...
... intersection of DE and IH , it is evi- dent , because of the parallel lines , that the three triangles PHM , PFE and MDI are equiangular . Therefore , all equiangular tri- angles being in the ratio of the squares of their homologous ...
Σελίδα 138
... intersect each other in a circle , are reciprocally proportional . Let the chords AB and CD intersect at F ; then will AF DF :: FC : FB . : Draw AC and BD . In the triangles AFC , DBF , the angles at F are equal , being vertical ; the ...
... intersect each other in a circle , are reciprocally proportional . Let the chords AB and CD intersect at F ; then will AF DF :: FC : FB . : Draw AC and BD . In the triangles AFC , DBF , the angles at F are equal , being vertical ; the ...
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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.