A Course of Mathematics: In Two Volumes. For the Use of the Royal Military Academy, Volume 1Gilberte and Rivington, 1841 - Mathematics |
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Page 307
... Rectangles that are contained by equal lines , are equal to each other . LET BD , FH , be two rectangles , having the sides AB , BC , equal to the sides EF , FG , each to each ; then will the rectangle BD be equal to the rectangle FH ...
... Rectangles that are contained by equal lines , are equal to each other . LET BD , FH , be two rectangles , having the sides AB , BC , equal to the sides EF , FG , each to each ; then will the rectangle BD be equal to the rectangle FH ...
Page 308
... rectangle AC of the two whole lines AD , AB ; and draw EG , FH , perpendicular to AB , or parallel to AD , to which they are equal ( th . 22 ) . Then the whole rectangle AC is made up of all the other rectangles AG , EH , FC : but these ...
... rectangle AC of the two whole lines AD , AB ; and draw EG , FH , perpendicular to AB , or parallel to AD , to which they are equal ( th . 22 ) . Then the whole rectangle AC is made up of all the other rectangles AG , EH , FC : but these ...
Page 309
... rectangles EF , DI : but GF is equal to the one line AC , and GE or FH is equal to the other line BC ; consequently the rectangle EF , contained under EG and GF , is equal to the rectangle of AC and BC . Again , FH being equal to CI or ...
... rectangles EF , DI : but GF is equal to the one line AC , and GE or FH is equal to the other line BC ; consequently the rectangle EF , contained under EG and GF , is equal to the rectangle of AC and BC . Again , FH being equal to CI or ...
Page 310
... rectangle contained by DH , or the sum of AB and AC , and by KD , or the difference of AB , and AC : therefore the difference of the squares of AB , AC , is equal to the rectangle under their sum and difference . THEOREM XXXIV . In any ...
... rectangle contained by DH , or the sum of AB and AC , and by KD , or the difference of AB , and AC : therefore the difference of the squares of AB , AC , is equal to the rectangle under their sum and difference . THEOREM XXXIV . In any ...
Page 311
... rectangle of the sum and difference of the two sides of any triangle , is equal to the rectangle of the sum and difference of the distances between the perpendicular and the two extremes of the base , or equal to the rectangle of the ...
... rectangle of the sum and difference of the two sides of any triangle , is equal to the rectangle of the sum and difference of the distances between the perpendicular and the two extremes of the base , or equal to the rectangle of the ...
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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