## A Course of Mathematics: In Two Volumes. Composed for the Use of the Royal Military Academy, Volume 1Longman, Orme & Company, 1841 - Mathematics |

### From inside the book

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Page 63

... Note . The denomination which occupies the place of inches in these products , means not square inches , but

... Note . The denomination which occupies the place of inches in these products , means not square inches , but

**rectangles**of an inch broad and a foot long . Thus , the answer to the first example is 29 sq . DUODECIMALS . 63 Duodecimals. Page 122

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**rectangle**of the sum and difference of two quantities is equal to the difference of their squares , some useful theorems obviously flow : viz . 1. a2 — b2 = ( a + b ) ( a − b ) . 2. a4 --- · b1 = ( a2 + b2 ) ( a2 — b2 ) = ( a2 + b2 ) ... Page 132

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**rectangle**of two lines , in the first ten propositions of the second book of Euclid , be exchanged for the term product of two numbers , and square on a line for the square of a number ; show that the propositions thus transformed are ... Page 293

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**rectangle**, square , rhombus , rhomboid . 38. A**rectangle**is a parallelogram , having a right angle . 39. A square is an equilateral**rectangle**; having its length and breadth equal , or all its sides equal , and all its angles equal ... Page 305

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**rectangle**. Cor . 2. Hence also , the sum of any two adjacent angles of a parallelogram is equal to two right angles . THEOREM XXIII . Every quadrilateral , whose opposite sides are equal , is a parallelogram , or has its opposite sides ...### Other editions - View all

### 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