Elements of Geometry and Trigonometry: With Applications in MensurationA.S. Barnes & Company, 1870 - 319 σελίδες |
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Σελίδα 19
... extremity C shall fall on the extremity F : then , since the sides are equal , A will fall on D. But since the angle C is equal to the angle F , the line CB Of Triangles . will fall on FE ; and since BOOK I. 19.
... extremity C shall fall on the extremity F : then , since the sides are equal , A will fall on D. But since the angle C is equal to the angle F , the line CB Of Triangles . will fall on FE ; and since BOOK I. 19.
Σελίδα 20
... extremity B will fall on E ; and consequently the side AB will fall on the side DE ( Ax . 11 ) . Hence , the two triangles will fill the same space , and consequently are equal ( Ax . 12. ) . A BD Scholium . Two triangles are said to be ...
... extremity B will fall on E ; and consequently the side AB will fall on the side DE ( Ax . 11 ) . Hence , the two triangles will fill the same space , and consequently are equal ( Ax . 12. ) . A BD Scholium . Two triangles are said to be ...
Σελίδα 38
... extremities of an arc , is called a chord . 6 A segment is the surface or portion of a circle included between an arc and its chord . Thus EFG is a segment . E E Б 3 Definitions . 7. A sector is the part of BOOK II Of the Circle, 39 23885.
... extremities of an arc , is called a chord . 6 A segment is the surface or portion of a circle included between an arc and its chord . Thus EFG is a segment . E E Б 3 Definitions . 7. A sector is the part of BOOK II Of the Circle, 39 23885.
Σελίδα 39
... extremities . CAB is a sector Thus , 8. A straight line is said to be in- scribed in a circle , when its extremities are in the circumference . Thus , the line AB is inscribed in a circle . 9. An inscribed angle is one which is formed ...
... extremities . CAB is a sector Thus , 8. A straight line is said to be in- scribed in a circle , when its extremities are in the circumference . Thus , the line AB is inscribed in a circle . 9. An inscribed angle is one which is formed ...
Σελίδα 41
... extremities . We shall then have , AD less than AC + CD ( Book I. Th . x * ) . But A AC + CD is equal to the diameter AB : hence , the chord AD is less than the diameter . THEOREM II . B If from the centre of a circle a line be drawn to ...
... extremities . We shall then have , AD less than AC + CD ( Book I. Th . x * ) . But A AC + CD is equal to the diameter AB : hence , the chord AD is less than the diameter . THEOREM II . B If from the centre of a circle a line be drawn to ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent angles allel alternate angles altitude angle ACB angles equal base multiplied bisect called centre chains chord circle whose diameter circumference cone consequently convex surface Cosine Cosine D Cotang cubic cylinder decimal diagonal dicular distance divided draw drawn equal Bk equal Th equal to half equivalent feet figure find the area frustum half the arc half the product hence horizontal hypothenuse inches included angle inscribed intersect Let ABC logarithm lower base M.
M. Sine measured by half Mensuration of Surfaces number of sides opposite angles outward angle parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane prism PROBLEM proportion quadrilateral radius ratio rectangle regular polygon Required the area rhombus right angled triangle right angles Th segment side AC similar similar triangles slant height solidity sphere straight line suppose Tang tangent THEOREM triangle ABC yards
Δημοφιλή αποσπάσματα
Σελίδα 48 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Σελίδα 12 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, etc.
Σελίδα 29 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 85 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Σελίδα 198 - To find the area of a trapezoid. RULE. Multiply the sum of the parallel sides by the perpendicular distance between them, and then divide the product by two : the quotient will be the area (Bk.
Σελίδα 159 - In every plane triangle there are six parts : three sides and three angles. These parts are so related to each other, that when one side and any two other parts are given, the remaining ones can be obtained, either by geometrical construction or by trigonometrical computation.
Σελίδα 187 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower Cway 33° 45' ; required the height of the tower.
Σελίδα 79 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 119 - If a cone be cut by a plane parallel to the base, the section will be a circle.