The elementary geometry of the right line and circle |
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Page viii
... segments and sectors of circle - and , also , the equality of the areas of parallelograms and triangles on the same or equal bases and between the same parallels . Thus , in the first four chapters , almost the whole substance ...
... segments and sectors of circle - and , also , the equality of the areas of parallelograms and triangles on the same or equal bases and between the same parallels . Thus , in the first four chapters , almost the whole substance ...
Page 18
... segments of circles ; but we apply it in the form of a supposed superposition of arcs and lines . It he portion of a circle on one side of a diameter be supposed turned round that diameter so that it may fall on the other side , the two ...
... segments of circles ; but we apply it in the form of a supposed superposition of arcs and lines . It he portion of a circle on one side of a diameter be supposed turned round that diameter so that it may fall on the other side , the two ...
Page 28
... segment less than a semicircle is Obtuse . From the first three cases , the angles at the centre , being less than two right angles , the arc ACB is greater than a semicircle , and the angles at the circumference are acute . Hence ...
... segment less than a semicircle is Obtuse . From the first three cases , the angles at the centre , being less than two right angles , the arc ACB is greater than a semicircle , and the angles at the circumference are acute . Hence ...
Page 30
... segment . Let AM be the tangent at A in the circle R , and AB the chord , making any angle , a , with AM , and also AC the diameter through A. Then , since CAM is a right angle ( last Theor . ) , the sum of a and 7 is a right angle ...
... segment . Let AM be the tangent at A in the circle R , and AB the chord , making any angle , a , with AM , and also AC the diameter through A. Then , since CAM is a right angle ( last Theor . ) , the sum of a and 7 is a right angle ...
Page 35
... segment . 4. To draw a line of a given magnitude PQ from a point O to a directive X. From the point O draw ( Prob . 2 ) a line OR equal to PQ . With O as centre and OR as radius , describe a circle cutting the directive X in A and B ...
... segment . 4. To draw a line of a given magnitude PQ from a point O to a directive X. From the point O draw ( Prob . 2 ) a line OR equal to PQ . With O as centre and OR as radius , describe a circle cutting the directive X in A and B ...
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The Elementary Geometry of the Right Line and Circle William Alexander Willock No preview available - 2022 |
Common terms and phrases
a₁ AB₁ acute angle ACB angle opposite B₁ BB₁ bisector C₁ Chap circumference coincide common chord construction describe a circle diameter 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 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 Let ABC line joining meet obtuse opposite angles pair of sides parallelogram perpendicular polygon Prob problem proved quadrilateral radii radius rectangle right angles right line semicircle sides AC sides equal six right 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 ?