The elementary geometry of the right line and circle |
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Page 34
... triangle ACB is the required equilateral triangle . For , since AC and BC , being radii of their respective circles , are each equal to the common radius AB , they are ( Ax . 1 ) equal to each other . There- fore the three sides of the ...
... triangle ACB is the required equilateral triangle . For , since AC and BC , being radii of their respective circles , are each equal to the common radius AB , they are ( Ax . 1 ) equal to each other . There- fore the three sides of the ...
Page 39
... angle . Therefore the radii RT and RT , are at right angles to OT and OT , respectively ... ACB will contain an angle a , equal to a . For , first , the angle BAC is by ... TRIANGLE AND PARALLELOGRAM . - THEOREMS THE CIRCLE - PROBLEMS . 39.
... angle . Therefore the radii RT and RT , are at right angles to OT and OT , respectively ... ACB will contain an angle a , equal to a . For , first , the angle BAC is by ... TRIANGLE AND PARALLELOGRAM . - THEOREMS THE CIRCLE - PROBLEMS . 39.
Page 40
... triangles and paral- lelograms . 1. The Angles at the base of an Isosceles Triangle opposite the Equal Sides are equal . a Let AB be the base , and AC , BC , the equal sides of the isosceles tri- angle ACB ; and let also the dotted ...
... triangles and paral- lelograms . 1. The Angles at the base of an Isosceles Triangle opposite the Equal Sides are equal . a Let AB be the base , and AC , BC , the equal sides of the isosceles tri- angle ACB ; and let also the dotted ...
Page 41
... triangle bisects the base , and is perpendicular to it . 2. The bisector of the base of an isosceles triangle is ... ACB be the triangle , and CP the perpendicular from the vertex Con AB . Then , if ACB be not isosceles , let CB be the ...
... triangle bisects the base , and is perpendicular to it . 2. The bisector of the base of an isosceles triangle is ... ACB be the triangle , and CP the perpendicular from the vertex Con AB . Then , if ACB be not isosceles , let CB be the ...
Page 42
... triangles are isosceles . Let AB be the common base , and ACB , AC , B the two tri- angles , and CC , the line bisecting both vertical angles Cand C. Then , if possible , suppose the triangle ACB not to be isosceles , and AC greater ...
... triangles are isosceles . Let AB be the common base , and ACB , AC , B the two tri- angles , and CC , the line bisecting both vertical angles Cand C. Then , if possible , suppose the triangle ACB not to be isosceles , and AC greater ...
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The Elementary Geometry of the Right Line and Circle William Alexander Willock No preview available - 2022 |
Common terms and phrases
acute angle ACB angles opposite B₁ BB₁ bisector C₁ Chap circumference coincide common base common chord construct describe a circle diameter directive directive X divided double draw duplicate ratio equal angles equal in area equal respectively equal sides equal Theor equal to BO equiangular equilateral triangle equisubmultiples Euclid external extremities figure four right angles geometry given circle given line given magnitude given point greater line greater segment half a right half difference half sum Hence hypothenuse inscribed internal angles intersection isosceles triangle joining the centres last Theor line joining meet obtuse opposite angles pair of sides parallel perpendicular polygon Prob problem proportional proved quadrilateral R₁ radii radius rectangle right angles right line semicircle sides AC sides equal six right squares squares of AO submultiple subtended suppose tangent theorem third triangle ACB triangle are equal vertex vertical angle
Popular passages
Page 6 - Things which are equal to the same thing are equal to one another. 2. 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.
Page 86 - Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians.
Page 115 - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 163 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth : or, if...
Page 43 - If two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less side.
Page 30 - The angle between a tangent to a circle and a chord through the point of contact is equal to the angle in the alternate segment.
Page 108 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 114 - If four quantities are in proportion, they will be in proportion by COMPOSITION; that is, the sum of the first and second, will be to the second, as the sum of the third and fourth, is to the fourth.
Page 66 - If a parallelogram and a triangle be on the same base and between the same parallels, the parallelogram shall be double of the triangle.
Page 84 - Thus, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, was an experimental discovery, or why did the discoverer sacrifice a hecatomb when he made out its proof ?