Elements of Geometry: With, Practical ApplicationsD. Appleton and Company, 1850 - 320 σελίδες |
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Σελίδα 18
With, Practical Applications George Roberts Perkins. AXIOMS . I. Things which are equal to the same thing , are equal to each other . II . When equals are added to equals , the whole are equal . III . When equals are taken from equals ...
With, Practical Applications George Roberts Perkins. AXIOMS . I. Things which are equal to the same thing , are equal to each other . II . When equals are added to equals , the whole are equal . III . When equals are taken from equals ...
Σελίδα 21
... equal . Let the two lines AB , CD inter- sect at the point F ; then will the angle AFC be equal to BFD , and the angle AFD equal to BFC . A- B F For , since the line CF meets the line AB , the two angles AFC , BFC , taken together , are ...
... equal . Let the two lines AB , CD inter- sect at the point F ; then will the angle AFC be equal to BFD , and the angle AFD equal to BFC . A- B F For , since the line CF meets the line AB , the two angles AFC , BFC , taken together , are ...
Σελίδα 22
... equal to the two sides and the included angle of the other , the triangles will be iden- tical , or equal in all respects . In the two triangles ABC , DFG , if the side CA be equal to the side GD , and the side CB equal to the side GF ...
... equal to the two sides and the included angle of the other , the triangles will be iden- tical , or equal in all respects . In the two triangles ABC , DFG , if the side CA be equal to the side GD , and the side CB equal to the side GF ...
Σελίδα 23
... equal to the angle BGD . B F Solution . Produce BD until DF is equal to BD : draw AF , cut- ting the mirror at G , and G will be the point required . For , com- paring the triangle GFD with GBD , we have DF equal to DB , DG common , and ...
... equal to the angle BGD . B F Solution . Produce BD until DF is equal to BD : draw AF , cut- ting the mirror at G , and G will be the point required . For , com- paring the triangle GFD with GBD , we have DF equal to DB , DG common , and ...
Σελίδα 24
... equal to DC , the side FD common , and the contained angle FDB equal to FDC , each being a right - angle . Therefore ( Prop . 11 , ) the triangle FBD is equal to FCD : consequently FB is equal to FC . The solution is ef- fected in the ...
... equal to DC , the side FD common , and the contained angle FDB equal to FDC , each being a right - angle . Therefore ( Prop . 11 , ) the triangle FBD is equal to FCD : consequently FB is equal to FC . The solution is ef- fected in 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.