## A Course of Mathematics: For the Use of Academies, as Well as Private Tuition ...S. Campbell & son, E. Duyckinck, 1822 - Mathematics |

### From inside the book

Page 291

... the sum of the angles of all the triangles is

... the sum of the angles of all the triangles is

**equal to twice as many right angles as the figure has sides**. But the sum of all the angles about the point P , which are so many many of the angles of the triangles , but no THEOREMS . 291. Page 292

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**equal to twice as many right angles as the figure has sides**, wanting the said four right an- gles . * Q. E. D. ...**equal to twice as many right angles as the figure has sides**. But the sum of all the inward angles , with four right ... Page 440

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**equal to twice as many right angles as the figure has sides**, wanting 4 right angles . But when there is an angle , as F. that bends inwards , and you measure the external angle , which is less than two right angles , subtract it which ...### Contents

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### Common terms and phrases

ABCD abscisses altitude arithmetical arithmetical mean arithmetical progression axis base bisected breadth caČ CDČ centre chord circle circumference circumscribed common cone consequently cube root curve cylinder DEČ decimal denominator denotes diameter difference distance divide divisor draw ellipse equation equiangular EXAM EXAMPLES feet figure fraction frustum Geom geometrical geometrical progression given number gives greater half height Hence improper fraction inches inscribed length Let ABC line drawn logarithm manner measure multiply ordinates parabola parallel parallelogram perimeter perpendicular plane polygon prism PROBLEM proportional Q. E. D. Corol Q. E. D. THEOREM quantity QUEST quotient radius ratio rectangle Reduce right angles right line right-angled triangle rule Scholium segment side Ac sine sphere square root subtract surd surface tangent theor theref triangle ABC VULGAR FRACTIONS yards

### Popular passages

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 292 - 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 2 - 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 189 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.

Page 293 - EBF, there are two angles in the one equal to two angles in the other, each to each ; and the...

Page 18 - The number to divide by, is the Divisor.- — And the number of times the dividend contains the divisor, is called the Quotient.

Page 280 - Similar figures, are those that have all the angles of the one equal to all the angles of the other, each to each, and the sides about the equal angles proportional.

Page 157 - Thus, the index or logarithm of 4, in the above series, is 2 ; and if this number be multiplied by 3, the product will be = 6 ; which is the logarithm of 64, or the third power of 4. And, if the logarithm of any number be divided by the index of its root, the quotient will be equal to the logarithm of that root.

Page 81 - Distinguish the given number into periods of two figures each, by putting a point over the place of units, another over the place of hundreds, and so on over every second figure, both to the left hand in integers, and to the right hand in decimals, which points will show the number of figures the root will consist of.

Page 278 - A Pentagon is a polygon of five sides ; a Hexagon, of six sides ; a Heptagon, seven; an Octagon, eight; a Nonagon, nine ; a Decagon, ten ; an Undecagon, eleven ; and 4 Dodecagon, twelve sides.