## A Course of Mathematics: For the Use of Academies, as Well as Private Tuition ... |

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Page 291

17 ) ; therefore the sum of the angles of all the triangles is

17 ) ; therefore 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 1 А A many of the angles of the triangles ,. Page 292

Hence it follows that the sum of all the inward angles of the polygon alone ato + c + o + e , is

Hence it follows that the sum of all the inward angles of the polygon alone ato + c + o + e , is

**equal to twice as many right angles as the figure has sides**, wanting the said four right angles . * Q. E. D. THEOREM XX . Page 440

To prove the work ; add all the inward angles A , B , C , & c . together ; for when the work is right , their sum will be

To prove the work ; add all the inward angles A , B , C , & c . together ; for when the work is right , their sum will be

**equal to twice as many right angles as the figure has sides**, wanting 4 right angles . But when there is an angle ...### What people are saying - Write a review

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### Common terms and phrases

added altitude Answer arithmetical axis base breadth called centre circle circumference common cone consequently contained Corol cube curve decimal denominator denotes diameter difference distance divide division divisor double draw drawn equal equation EXAMPLES extremes feet figure former four fraction given gives greater greatest half height Hence inches interest join length less letters logarithm manner mean measure meet method multiply namely Note opposite parallel parallelogram perpendicular plane polygon position PROBLEM proportional quantity Quest quotient radius ratio rectangle Reduce remainder right angles root rule segment sides similar solid square square root subtract Suppose surface taken tangent theor THEOREM theref thing third triangle whole yards

### Popular passages

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 290 - 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 291 - 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 278 - 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 276 - 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.