## A Course of Mathematics for the Use of Academies: As Well as Private Tuition |

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### Contents

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### Common terms and phrases

ABCD abscisses altitude arithmetical arithmetical mean arithmetical progression axis base bisected breadth centre chord circle circumference circumscribed common compound cone conjugate hyperbolas consequently Corol cube root curve cylinder decimal denominator denotes diameter difference distance divide divisor draw e. d. THEOREM ellipse equation equiangular equilateral Exam EXAMPLES feet figure fraction frustum Geom geometrical geometrical progression given number gives greater height Hence improper fraction inches infinite series inscribed length line drawn logarithm manner multiply number of terms ordinates parabola parallel parallelogram perimeter perpendicular plane polygon prism PROBLEM proportional quantity Quest quotient radius ratio rectangle Reduce remainder right angles right line right-angled triangle rule Scholium segment side AC sine solid sphere square root subtract surd surface tangent theor theref triangle abc VULGAR FRACTIONS whole number yards

### Popular passages

Page 2 - Thus, when it is said that, The sum of the three angles of any triangle is equal to two right angles, this is a Theorem, the truth of which is demonstrated by Geometry.

Page 4 - Los números cardinales 0: zero 1: one 2: two 3: three 4: four 5: five 6: six 7: seven 8: eight 9: nine 10: ten 11: eleven 12: twelve 13: thirteen 14: fourteen 15: fifteen 16: sixteen 17: seventeen 18: eighteen 19: nineteen 20: twenty...

Page ii - District, has deposited in this office the title of a book, the right whereof he claims as proprietor, in the words following, to wit : " THE CHILD'S BOTANY," In conformity to the act of the Congress of the United States, entitled, " An act for the encouragement of learning by securing the copies of maps, charts, and books to the authors and proprietors of such copies, during the times therein mentioned...

Page 298 - If a straight line be divided into any two parts, the square on the whole line is...

Page 440 - 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.

Page 287 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.

Page 312 - The angle formed by a tangent to a circle, and a chord drawn from the point of contact, is equal to the angle in the alternate segment.

Page 287 - AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side.

Page 281 - If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.

Page 400 - Two ships of war, intending to cannonade a fort, are, by the shallowness of the water, kept so far from it, that they suspect their guns cannot reach it with effect. In order, therefore, to measure the distance, they separate from each other a quarter of a mile, or 440 yards ; then each ship observes and measures the angle which the other ship and the fort subtend, which angles are 83° 45