The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry from the Edition of Dr. Robert Simson ... With Exercises. By S. A. Good ... Second EditionCharles Henry Law, 1854 - 120 σελίδες |
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Σελίδα 23
... AC , are greater than BE , EC ; much more then 5. BA , AC , are greater than BD , DC . Again , because the exterior ... straight lines , but any two whatever of these must be greater than the third , ( I. 20. ) Let A , B , C , be the ...
... AC , are greater than BE , EC ; much more then 5. BA , AC , are greater than BD , DC . Again , because the exterior ... straight lines , but any two whatever of these must be greater than the third , ( I. 20. ) Let A , B , C , be the ...
Σελίδα 24
... straight lines A , B , C. Which was to be done . PROP . XXIII . — PROBLEM . At a given point in a given straight line ... AC , equal to the two DE , DF , each to each , viz . AB equal to DE , and AC to DF ; but the angle BAC greater than the ...
... straight lines A , B , C. Which was to be done . PROP . XXIII . — PROBLEM . At a given point in a given straight line ... AC , equal to the two DE , DF , each to each , viz . AB equal to DE , and AC to DF ; but the angle BAC greater than the ...
Σελίδα 25
... straight line DE , make ( I. 23. ) the angle EDG equal to the angle BAC ; and make DG equal ( I. 3. ) to AC or DF , and join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC , are equal to the two ED , DG ...
... straight line DE , make ( I. 23. ) the angle EDG equal to the angle BAC ; and make DG equal ( I. 3. ) to AC or DF , and join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC , are equal to the two ED , DG ...
Σελίδα 31
... straight line AB ; and because AB is parallel to CE , and AC meets them , ( I. 29. ) 1. The alternate angles BAC , ACE , are equal . Again , because AB is parallel to CE , and BD falls upon them , 2. The exterior angle ECD is equal to ...
... straight line AB ; and because AB is parallel to CE , and AC meets them , ( I. 29. ) 1. The alternate angles BAC , ACE , are equal . Again , because AB is parallel to CE , and BD falls upon them , 2. The exterior angle ECD is equal to ...
Σελίδα 33
... straight line BC meets the two straight lines AC , BD , and makes the alternate angles ACB , CBD , equal to one another , ( I. 27. ) 4. AC is parallel to BD ; and it was shown to be equal to it . Therefore , straight lines , & c ...
... straight line BC meets the two straight lines AC , BD , and makes the alternate angles ACB , CBD , equal to one another , ( I. 27. ) 4. AC is parallel to BD ; and it was shown to be equal to it . Therefore , straight lines , & c ...
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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