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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 11.
Σελίδα 4
... unequal sides . XXVII . A right - angled triangle is that which has a right angle . XXVIII . An obtuse - angled triangle is that which has an obtuse angle . XXIX . An acute - angled triangle is that which has three acute angles . XXX ...
... unequal sides . XXVII . A right - angled triangle is that which has a right angle . XXVIII . An obtuse - angled triangle is that which has an obtuse angle . XXIX . An acute - angled triangle is that which has three acute angles . XXX ...
Σελίδα 6
... unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are double of the same , are equal to one another . VII . Things which are halves of the same , are equal to one another . VIII . Magnitudes ...
... unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are double of the same , are equal to one another . VII . Things which are halves of the same , are equal to one another . VIII . Magnitudes ...
Σελίδα 11
... unequal to AC ; that is , it is equal to it . Wherefore , if two angles , & c . q.E.D. COR . - Hence every equiangular triangle is also equilateral . PROP . VII . — THEOREM . Upon the same base , and on the same side of it , there ...
... unequal to AC ; that is , it is equal to it . Wherefore , if two angles , & c . q.E.D. COR . - Hence every equiangular triangle is also equilateral . PROP . VII . — THEOREM . Upon the same base , and on the same side of it , there ...
Σελίδα 27
... unequal to DE , that is , it is equal to it ; and BC is equal ( Hyp . ) to EF ; therefore 6. The two AB , BC , are equal to the two DE , EF , each to each ; and the angle ABC is equal ( Hyp . ) to the angle DEF ; therefore ( I. 4. ) 7 ...
... unequal to DE , that is , it is equal to it ; and BC is equal ( Hyp . ) to EF ; therefore 6. The two AB , BC , are equal to the two DE , EF , each to each ; and the angle ABC is equal ( Hyp . ) to the angle DEF ; therefore ( I. 4. ) 7 ...
Σελίδα 30
... unequal to the angle GHD , that is , it is equal to it ; but ( I. 15. ) the angle AGH is equal to the angle EGB ; therefore likewise 5. EGB is equal to GHD ; add to each of these the angle BGH ; therefore 6. The angles EGB , BGH , are ...
... unequal to the angle GHD , that is , it is equal to it ; but ( I. 15. ) the angle AGH is equal to the angle EGB ; therefore likewise 5. EGB is equal to GHD ; add to each of these the angle BGH ; therefore 6. The angles EGB , BGH , are ...
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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 THEOREM touches the circle triangle ABC twice the rectangle