The elementary geometry of the right line and circle |
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Page viii
... placed between two com- paratively easy ones , is out of place , and has been a sore stumbling - block to young beginners . Its subject- matter is here held back for the Fifth Chapter , not on account of this difficulty , but because ...
... placed between two com- paratively easy ones , is out of place , and has been a sore stumbling - block to young beginners . Its subject- matter is here held back for the Fifth Chapter , not on account of this difficulty , but because ...
Page ix
William Alexander Willock. never have been disassociated . It is evident that Euclid placed it in his First Book solely with a view to prove the ninth and tenth theorems of his Second , which , however , could have been easily proved ...
William Alexander Willock. never have been disassociated . It is evident that Euclid placed it in his First Book solely with a view to prove the ninth and tenth theorems of his Second , which , however , could have been easily proved ...
Page 8
... placed in advance of or beside the arrowheads , and are used in the course of demonstration generally to represent the directives ; but in particular cases , where it tends to simplifica- tion , they are also used with two other letters ...
... placed in advance of or beside the arrowheads , and are used in the course of demonstration generally to represent the directives ; but in particular cases , where it tends to simplifica- tion , they are also used with two other letters ...
Page 16
... placed within the polygon , draw A ΛΑΙ ΕΙ DI BI lines OA , OB1 , OC1 , & c . , parallel to the sides of the poly- gon . Then , since OA , is parallel to EA , and OB1 to AB , the angle A , OB , is ( by Parallelism ) equal to the angle a ...
... placed within the polygon , draw A ΛΑΙ ΕΙ DI BI lines OA , OB1 , OC1 , & c . , parallel to the sides of the poly- gon . Then , since OA , is parallel to EA , and OB1 to AB , the angle A , OB , is ( by Parallelism ) equal to the angle a ...
Page 21
... placed below NM , it will then coincide with the semi - circle NBM . But in this superposition AP being at right angles to RP will turn round NM so as to cover BP ; and the point A will coincide with B. 1. The lines AP and BP are ...
... placed below NM , it will then coincide with the semi - circle NBM . But in this superposition AP being at right angles to RP will turn round NM so as to cover BP ; and the point A will coincide with B. 1. The lines AP and BP are ...
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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 ?