A Course of Mathematics: In Two Volumes. Composed for the Use of the Royal Military Academy, Volume 1Longman, Orme & Company, 1841 - Mathematics |
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Page 302
... meeting two other lines , make the angles on the same side of it equal , those two lines are parallels . Cor . 2. If a line , cutting two other lines , make the sum of the two inward angles on the same side , less than two right angles ...
... meeting two other lines , make the angles on the same side of it equal , those two lines are parallels . Cor . 2. If a line , cutting two other lines , make the sum of the two inward angles on the same side , less than two right angles ...
Page 304
... meeting another ( th . 4 ) . And there being as many outward , or inward angles , as the figure has sides ; therefore the sum of all the inward and outward angles , is equal to twice as many right angles as the figure has sides . But ...
... meeting another ( th . 4 ) . And there being as many outward , or inward angles , as the figure has sides ; therefore the sum of all the inward and outward angles , is equal to twice as many right angles as the figure has sides . But ...
Page 312
... meeting the parallels AB , DC , make the angle BAE equal to the angle DCE , and the angle ABE equal to the angle CDE , and the side AB equal to the side DC ( th . 22 ) ; there- fore these two triangles are identical , and have their ...
... meeting the parallels AB , DC , make the angle BAE equal to the angle DCE , and the angle ABE equal to the angle CDE , and the side AB equal to the side DC ( th . 22 ) ; there- fore these two triangles are identical , and have their ...
Page 316
... meeting FG , makes the sum of the two angles at E equal to two right angles ( th . 6 ) , and the line CD makes with AB the sum of the two angles at C equal to two right angles ; if from these two equal sums there be taken away the parts ...
... meeting FG , makes the sum of the two angles at E equal to two right angles ( th . 6 ) , and the line CD makes with AB the sum of the two angles at C equal to two right angles ; if from these two equal sums there be taken away the parts ...
Page 320
... meeting a circle each in two points , cut one another , either within it or without it ; the rectangle of the parts of the one , is equal to the rectangle of the parts of the other ; the parts of each being measured from the point of ...
... meeting a circle each in two points , cut one another , either within it or without it ; the rectangle of the parts of the one , is equal to the rectangle of the parts of the other ; the parts of each being measured from the point of ...
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Common terms and phrases
ABCD algebraic altitude arithmetical arithmetical progression base bisect breadth centre chord circle circumference coefficients common cone cosec cube root decimal denominator denoted diagonal diameter difference dihedral angle distance divided divisor draw drawn equal equation equiangular EXAMPLES expression figure fraction frustum geometrical given line greater hence inscribed integer intersection join length less lineation logarithms mantissa measure meeting method multiplied parallel parallel ruler parallelogram perpendicular plane polygon prism PROBLEM proportional quantity quotient radii radius ratio rectangle Reduce right angles rule Scholium segment sides sine solid angle solution square root straight line subtraction tangent THEOREM third trapezium triangle ABC u₁ vulgar fraction Whence