A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 31
... Describe on it an equi- lateral triangle ABC [ I. 1 ] , and bisect the angle ACB by the straight line CD . [ I. 9. ] AB shall be cut into two equal A parts at the point D. D Because AC is equal to CB [ Def . 24 ] , and CD 3 . is common ...
... Describe on it an equi- lateral triangle ABC [ I. 1 ] , and bisect the angle ACB by the straight line CD . [ I. 9. ] AB shall be cut into two equal A parts at the point D. D Because AC is equal to CB [ Def . 24 ] , and CD 3 . is common ...
Página 32
... describe the equilateral triangle DFE [ I . 1 ] , and join CF. The straight line CF drawn from the given point CA shall be at right angles to the given straight line AB . B Because DC is equal to CE [ Con . ] , and FC is 3 . common to ...
... describe the equilateral triangle DFE [ I . 1 ] , and join CF. The straight line CF drawn from the given point CA shall be at right angles to the given straight line AB . B Because DC is equal to CE [ Con . ] , and FC is 3 . common to ...
Página 33
... describe A H the circle EGF , meeting AB in F and G. [ Post . 3. ] Bisect FG in H [ I. 10 ] , and join CH . The straight line CH drawn from the given point C shall be perpen- dicular to the given straight line AB . Join CF , CG ...
... describe A H the circle EGF , meeting AB in F and G. [ Post . 3. ] Bisect FG in H [ I. 10 ] , and join CH . The straight line CH drawn from the given point C shall be perpen- dicular to the given straight line AB . Join CF , CG ...
Página 34
... describe an arc CG . In AD take a point E ; join EC and describe an arc cutting the former arc in G. Join CG , which shall be perpendicular to AB . Join EG and DG . The proof is identical with exercise 2 to prop . 9 . Ex . From a given ...
... describe an arc CG . In AD take a point E ; join EC and describe an arc cutting the former arc in G. Join CG , which shall be perpendicular to AB . Join EG and DG . The proof is identical with exercise 2 to prop . 9 . Ex . From a given ...
Página 44
... describe the circle DKL . [ Post . 3. ] From the centre G , at the dis- tance GH , describe the circle HKL . Join KF , KG . The triangle KFG shall have its sides equal to the three straight lines A , B , C. 3 . Because the point F is ...
... describe the circle DKL . [ Post . 3. ] From the centre G , at the dis- tance GH , describe the circle HKL . Join KF , KG . The triangle KFG shall have its sides equal to the three straight lines A , B , C. 3 . Because the point F is ...
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A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles are equal angles CEA axioms base BC bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join less Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal