The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 Seiten |
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... straight line , or Any two angles of a triangle are together less than two right angles . After the general ... given straight line : it is required to describe an equilateral triangle on AB . The construction then usually follows ...
... straight line , or Any two angles of a triangle are together less than two right angles . After the general ... given straight line : it is required to describe an equilateral triangle on AB . The construction then usually follows ...
Seite 7
Isaac Todhunter. PROPOSITION 1. PROBLEM . To describe an equilateral triangle on a given finite straight line . Let AB be the given straight line : it is required to describe an equilateral triangle on AB . A E From the centre A , at the ...
Isaac Todhunter. PROPOSITION 1. PROBLEM . To describe an equilateral triangle on a given finite straight line . Let AB be the given straight line : it is required to describe an equilateral triangle on AB . A E From the centre A , at the ...
Seite 8
Isaac Todhunter. PROPOSITION 2. PROBLEM . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line it is required to draw from the point A a straight line equal ...
Isaac Todhunter. PROPOSITION 2. PROBLEM . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line it is required to draw from the point A a straight line equal ...
Seite 9
... straight line AD equal to C ; [ I. 2 . and from the centre A , at the distance AD , describe the circle DEF meeting ... given straight lines a part AE has been cut off equal to C the less . Q.E.F. PROPOSITION 4 . THEOREM . If two ...
... straight line AD equal to C ; [ I. 2 . and from the centre A , at the distance AD , describe the circle DEF meeting ... given straight lines a part AE has been cut off equal to C the less . Q.E.F. PROPOSITION 4 . THEOREM . If two ...
Seite 15
... given rectilineal angle BAC is bisected by the straight line AF . Q.E.F. PROPOSITION 10. PROBLEM , To bisect a given finite straight line , that is to divide it into two equal parts . Let AB be ... draw a straight line at BOOK I. 9 , 10 . 15.
... given rectilineal angle BAC is bisected by the straight line AF . Q.E.F. PROPOSITION 10. PROBLEM , To bisect a given finite straight line , that is to divide it into two equal parts . Let AB be ... draw a straight line at BOOK I. 9 , 10 . 15.
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ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore