The elementary geometry of the right line and circle |
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Page vii
... equal , which greater , and which less ? Thus the directive should precede ... equal triangles - also to the relations of the sides and angles of ... area . They are confined to the right line and circle in their relations of ...
... equal , which greater , and which less ? Thus the directive should precede ... equal triangles - also to the relations of the sides and angles of ... area . They are confined to the right line and circle in their relations of ...
Page viii
... Area is , for the first time , introduced in the Fourth Chapter , in which it is considered , by the aid of Euclid's principle of superposition , in reference to areas generally , to the equality of the areas in the several cases of equal ...
... Area is , for the first time , introduced in the Fourth Chapter , in which it is considered , by the aid of Euclid's principle of superposition , in reference to areas generally , to the equality of the areas in the several cases of equal ...
Page 63
... equal , the result is that all sides and angles are equal respectively . It is sufficient , therefore , to prove that , when the three pairs of sides of two triangles are equal respectively , the areas of the triangles are equal . In ...
... equal , the result is that all sides and angles are equal respectively . It is sufficient , therefore , to prove that , when the three pairs of sides of two triangles are equal respectively , the areas of the triangles are equal . In ...
Page 64
William Alexander Willock. 2. Two Segments of the Same Circle , or of two equal circles , enclosed by two Equal Arcs and their Chords are equal in area . Let the segments ACB and A , C , B , be first taken in the circle A AI B R --N- RI ...
William Alexander Willock. 2. Two Segments of the Same Circle , or of two equal circles , enclosed by two Equal Arcs and their Chords are equal in area . Let the segments ACB and A , C , B , be first taken in the circle A AI B R --N- RI ...
Page 65
... areas of the segments and of the triangles , are equal , as stated . In the case of the sectors being one in each of two equal circles , the proof is the same . The segments are equal in area , as proved in the last theorem ; and the ...
... areas of the segments and of the triangles , are equal , as stated . In the case of the sectors being one in each of two equal circles , the proof is the same . The segments are equal in area , as proved in the last theorem ; and the ...
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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 ?