# A Course of Mathematics for the Use of Academies: As Well as Private Tuition, Volume 1

S. Campbell, 1825 - Mathematics
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### Contents

 OF VOLUME 1 Roman Notation 7 Multiplication 13 Reduction 23 Compound Addition 32 Golden Rule or Rule of Three 44 Vulgar Fractions 51 Subtraction of Vulgar Fractions 62
 Piling of Balls 223 223 Simple Equations 230 Quadratic Equalions 249 Resolution of Cubic and Higher Equations 257 Simple Interest 266 GEOMETRY 275 AriomsTheorems 281 Of Ratios and Proportions 319

 Subtraction of Decimals 68 Rule of Three in Decimals 76 To extract the Cube Root 85 Ratios Proportions and Progressions 110 Geometrical Progression 116 Double Fellowship 122 Alligation Medial 129 Single Position 135 Practical Questions 150 To compute Logarithms 159 Multiplication by Logarithms 167 Addition 175 Multiplication 181 Algebraic Fractions 188 Involution 199 Surds 206 Infinite Series 213
 of Planes and SolidsDefinitions 336 Problems 353 Applications of Algebra to Geometry 369 Plane Trigonometry 377 Heights and Distances 393 Mensuration of Planes 402 Mensuration of Solids 419 Land Surveying 429 Artificers Work 458 Timber Measuring 466 of the Ellipse 473 of the Hyperbola 491 of the Parabola 514 of the Conic Sections as expressed by Algebraic equations called 532 Problems relative to the Division of Surfaces 558 Construction of Geometrical Problems 571

### 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 n�meros 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 296 - If a straight line be divided into any two parts, the square on the whole line is...
Page 438 - 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 285 - 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 310 - 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 285 - AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side.
Page 279 - 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 398 - 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