Elements of Geometry: With, Practical ApplicationsD. Appleton and Company, 1850 - 320 σελίδες |
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Σελίδα 24
... Suppose AC to be a tree , standing on the horizontal plane AB ; it is required to find at what point it must be broken , so that , by falling , the top may strike the ground at B. A D B Solution . Join CB , and bisect it by the ...
... Suppose AC to be a tree , standing on the horizontal plane AB ; it is required to find at what point it must be broken , so that , by falling , the top may strike the ground at B. A D B Solution . Join CB , and bisect it by the ...
Σελίδα 55
... suppose a = 6 ; b = 4 ; and we find ( 6 + 4 ) == 10262 + 2.6 × 4 + 42 = 36 + 48 + 16 = 100 . ( 46. ) This theorem may be generalized , so as to apply in the case of a line which is the sum of any number of parts . Let the line AB be ...
... suppose a = 6 ; b = 4 ; and we find ( 6 + 4 ) == 10262 + 2.6 × 4 + 42 = 36 + 48 + 16 = 100 . ( 46. ) This theorem may be generalized , so as to apply in the case of a line which is the sum of any number of parts . Let the line AB be ...
Σελίδα 65
... + BC AC - BC - AD + BD AD - BD or , ( AC ÷ BC ) ( AC — BC ) = AB ( AD — BD ; ) [ 1st fig . ] and ( AC + BC ) ( AC — BC ) = AB ( AD + BD . ) [ 2d fig . ] ( 58. ) As an illustration , suppose the length 6 * BOOK II . 65 PROPOSITION IX. ...
... + BC AC - BC - AD + BD AD - BD or , ( AC ÷ BC ) ( AC — BC ) = AB ( AD — BD ; ) [ 1st fig . ] and ( AC + BC ) ( AC — BC ) = AB ( AD + BD . ) [ 2d fig . ] ( 58. ) As an illustration , suppose the length 6 * BOOK II . 65 PROPOSITION IX. ...
Σελίδα 66
... suppose the length of the lines to be as denoted in the diagrams , we find in each triangle 172-102 = 152-62 17 17 10 8 10 15 Ꮽ D 6 B 6 ( 59. ) From this proposition , we may readily deduce a method of determining the area of a ...
... suppose the length of the lines to be as denoted in the diagrams , we find in each triangle 172-102 = 152-62 17 17 10 8 10 15 Ꮽ D 6 B 6 ( 59. ) From this proposition , we may readily deduce a method of determining the area of a ...
Σελίδα 85
... suppose the tangent DF to pass through the angular point A. Then , the angle DAC being measured by half the arc half the arc AB , ( B. III D B D ABC , and the angle DAB by Prop . vI , ) it follows that the difference of those angles is ...
... suppose the tangent DF to pass through the angular point A. Then , the angle DAC being measured by half the arc half the arc AB , ( B. III D B D ABC , and the angle DAB by Prop . vI , ) it follows that the difference of those angles is ...
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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.