Elements of Geometry: With, Practical ApplicationsD. Appleton and Company, 1850 - 320 σελίδες |
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Σελίδα 13
... consequently some feelings of pain . XII . Two straight lines are said to be parallel , when , being situated in the same plane , they cannot meet , how far soever , either way , both of them be produced . They are obviously everywhere ...
... consequently some feelings of pain . XII . Two straight lines are said to be parallel , when , being situated in the same plane , they cannot meet , how far soever , either way , both of them be produced . They are obviously everywhere ...
Σελίδα 22
... consequently the side AB will coincide with DF . Therefore the two triangles are iden- tical , and have all their other corresponding parts equal , ( Ax . IX , ) namely , the side AB equal to the side DF , the angle A equal to the angle ...
... consequently the side AB will coincide with DF . Therefore the two triangles are iden- tical , and have all their other corresponding parts equal , ( Ax . IX , ) namely , the side AB equal to the side DF , the angle A equal to the angle ...
Σελίδα 23
... consequently the angle DGB is equal to the angle DGF : but DGF is equal to the opposite angle AGC , ( Prop . 11 :) hence the angle BGD is equal to AGC . Which is necessary , that the angle of incidence and the angle of reflection of the ...
... consequently the angle DGB is equal to the angle DGF : but DGF is equal to the opposite angle AGC , ( Prop . 11 :) hence the angle BGD is equal to AGC . Which is necessary , that the angle of incidence and the angle of reflection of the ...
Σελίδα 24
... consequently FB is equal to FC . The solution is ef- fected in the same way when the tree is supposed to stand upon an inclined sur- face , as upon the side of a hill . A A B ( 34. ) The general proposition , of which the foregoing are ...
... consequently FB is equal to FC . The solution is ef- fected in the same way when the tree is supposed to stand upon an inclined sur- face , as upon the side of a hill . A A B ( 34. ) The general proposition , of which the foregoing are ...
Σελίδα 25
... of the side DG ; also , since the angle F is equal to the angle B , the side BC will take the direction of the side FG ; consequently the point C must coincide with : the point G. Therefore the two triangles are identical . 3 BOOK I. 25 ...
... of the side DG ; also , since the angle F is equal to the angle B , the side BC will take the direction of the side FG ; consequently the point C must coincide with : the point G. Therefore the two triangles are identical . 3 BOOK I. 25 ...
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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.