Elements of Geometry: With, Practical ApplicationsD. Appleton and Company, 1850 - 320 σελίδες |
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Αποτελέσματα 1 - 5 από τα 33.
Σελίδα 18
... double of the same or equal things , are equal . VII . Things which are halves of the same thing , are equal . VIII . Every whole is equal to all its parts taken to- gether , and greater than any of them . IX . Things which coincide ...
... double of the same or equal things , are equal . VII . Things which are halves of the same thing , are equal . VIII . Every whole is equal to all its parts taken to- gether , and greater than any of them . IX . Things which coincide ...
Σελίδα 60
... double the triangle ACD , on the same base AD , and between the same parallels AD , CM ; and since the doubles of equal things are equal , ( Ax . VI , ) it follows that the square AH is equal to the parallelogram AM . In like manner ...
... double the triangle ACD , on the same base AD , and between the same parallels AD , CM ; and since the doubles of equal things are equal , ( Ax . VI , ) it follows that the square AH is equal to the parallelogram AM . In like manner ...
Σελίδα 61
... double the square itself . Cor . 4. The sum of the squares of the sides of a rect- angle is equal to the sum of the squares of the diagonals . ( 50. ) This theorem may be demonstrated in the following man- ner : Let ABC be a right ...
... double the square itself . Cor . 4. The sum of the squares of the sides of a rect- angle is equal to the sum of the squares of the diagonals . ( 50. ) This theorem may be demonstrated in the following man- ner : Let ABC be a right ...
Σελίδα 62
... double the triangle ACB , ( B. II , Prop . 11 :) hence , the squares AF and BH are together also equal to the whole space ADKGB diminished by three times the triangle ACB , and consequently these two squares are equivalent to the square ...
... double the triangle ACB , ( B. II , Prop . 11 :) hence , the squares AF and BH are together also equal to the whole space ADKGB diminished by three times the triangle ACB , and consequently these two squares are equivalent to the square ...
Σελίδα 69
... , by the aid of the fol- lowing diagrams : 17 10 10 15 9 A B 6 Thus , 102 = 212 + 172 − 2.21 × 15 ; 10292 + 172-2 . 9 × 15 . [ 1st figure . ] [ 2d figure . ] PROPOSITION XII THEOREM . In any triangle , the double BOOK II . 69.
... , by the aid of the fol- lowing diagrams : 17 10 10 15 9 A B 6 Thus , 102 = 212 + 172 − 2.21 × 15 ; 10292 + 172-2 . 9 × 15 . [ 1st figure . ] [ 2d figure . ] PROPOSITION XII THEOREM . In any triangle , the double BOOK II . 69.
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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.