A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 30
... Join AF . The straight line AF shall bi- sect the angle BAC . 3 . Because AD is equal to AE [ Con . ] , and AF is ... joining their vertices will bisect their common base at right angles . [ See fig . to the prop . ] 2. If the triangles ...
... Join AF . The straight line AF shall bi- sect the angle BAC . 3 . Because AD is equal to AE [ Con . ] , and AF is ... joining their vertices will bisect their common base at right angles . [ See fig . to the prop . ] 2. If the triangles ...
Página 32
... 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 the two triangles DCF , ECF ; the two sides DC , CF are ...
... 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 the two triangles DCF , ECF ; the two sides DC , CF are ...
Página 33
... 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 . Because FH is equal to HG [ Const . ] , and HC is 3 . common to the two triangles FHC , GHC ; the two ...
... 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 . Because FH is equal to HG [ Const . ] , and HC is 3 . common to the two triangles FHC , GHC ; the two ...
Página 34
... 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 point to draw a straight line equally inclined to two given straight lines which cut one another ...
... 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 point to draw a straight line equally inclined to two given straight lines which cut one another ...
Página 38
... join BE and produce it to F , making EF equal to EB , [ I. 3. ] and join FC . Because AE is equal to EC , and BE to EF ; 3. [ Const . ] the two sides AE , EB are equal to the two sides CE , EF , each to each ; and the angle AEB is equal ...
... join BE and produce it to F , making EF equal to EB , [ I. 3. ] and join FC . Because AE is equal to EC , and BE to EF ; 3. [ Const . ] the two sides AE , EB are equal to the two sides CE , EF , each to each ; and the angle AEB is equal ...
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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