The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry, from the Edition of Dr. Robert Simson ... With ExercisesCharles Henry Law, 1854 - 120 páginas |
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Página 19
Euclid, Samuel A. GOOD. Take away the common angle AED , and ( Ax . 3. ) 4 . The remaining angle CEA is equal to the remaining angle DEB . In the same manner it can be demonstrated that 5. The angles CEB , 4ED , are equal . Therefore ...
Euclid, Samuel A. GOOD. Take away the common angle AED , and ( Ax . 3. ) 4 . The remaining angle CEA is equal to the remaining angle DEB . In the same manner it can be demonstrated that 5. The angles CEB , 4ED , are equal . Therefore ...
Página 23
... Take a straight line_DE terminated at the point D , but unlimited towards E , and make ( I. 3. ) DF equal to A , FG equal to B , and GH equal to C ; and from the centre F , at a distance FD , describe ( Post . 3. ) the circle DKL ; and ...
... Take a straight line_DE terminated at the point D , but unlimited towards E , and make ( I. 3. ) DF equal to A , FG equal to B , and GH equal to C ; and from the centre F , at a distance FD , describe ( Post . 3. ) the circle DKL ; and ...
Página 24
... Take in CD , CE , any points D , E , and join DE ; and make ( I. 22. ) the triangle AFG , the sides of which shall be equal to the three straight lines CD , DE , CE , so that CD be equal to AF , CE to AG , and DE to FG ; the angle FAG ...
... Take in CD , CE , any points D , E , and join DE ; and make ( I. 22. ) the triangle AFG , the sides of which shall be equal to the three straight lines CD , DE , CE , so that CD be equal to AF , CE to AG , and DE to FG ; the angle FAG ...
Página 29
... Take away the common angle BGH ; therefore 2. The remaining angle AGH is equal to the remaining angle GHD , and they are alternate angles ; therefore ( I. 27. ) 3. AB is parallel to CD . Wherefore if a straight line , & c . Q.E.D. PROP ...
... Take away the common angle BGH ; therefore 2. The remaining angle AGH is equal to the remaining angle GHD , and they are alternate angles ; therefore ( I. 27. ) 3. AB is parallel to CD . Wherefore if a straight line , & c . Q.E.D. PROP ...
Página 31
... take any point D , and join AD ; and at the point 4 , in the straight line AD , make ( I. 23. ) the angle DAE equal to the angle ADC ; and produce the straight line EA to F ; EF is parallel to BC . E F B D Because the straight line AD ...
... take any point D , and join AD ; and at the point 4 , in the straight line AD , make ( I. 23. ) the angle DAE equal to the angle ADC ; and produce the straight line EA to F ; EF is parallel to BC . E F B D Because the straight line AD ...
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Términos y frases comunes
AB is equal AC is equal adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal base BC bisected circle ABC circumference diameter double draw equal angles equal Constr equal Hyp equal straight lines equal to BC equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite less Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F produced Q.E.D. PROP rectangle AE rectangle contained remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC straight line drawn touches the circle triangle ABC twice the rectangle