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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Σελίδα 2
... . XI . An obtuse angle is that which is greater than a right angle . XII . An acute angle is that which is less than a right angle . XIII . is the extremity of any thing . ” 辈 XIV . A figure is that which is inclosed 2 EUCLID'S ELEMENTS .
... . XI . An obtuse angle is that which is greater than a right angle . XII . An acute angle is that which is less than a right angle . XIII . is the extremity of any thing . ” 辈 XIV . A figure is that which is inclosed 2 EUCLID'S ELEMENTS .
Σελίδα 6
... greater than its part . IX . X. Two straight lines cannot inclose a space . XI . All right angles are equal to one another . XII . " If a straight line meet two straight lines , so as to make the two interior angles on the same side of ...
... greater than its part . IX . X. Two straight lines cannot inclose a space . XI . All right angles are equal to one another . XII . " If a straight line meet two straight lines , so as to make the two interior angles on the same side of ...
Σελίδα 8
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point 4 , draw ( I. 2. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( Post . 3. ) the ...
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point 4 , draw ( I. 2. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( Post . 3. ) the ...
Σελίδα 10
... greater , cut off AG equal ( I. 3. ) to AF , the less , and join FC , GB . Because AF is equal ( Constr . ) to 4G , and AB ( Hypothesis ) to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the ...
... greater , cut off AG equal ( I. 3. ) to AF , the less , and join FC , GB . Because AF is equal ( Constr . ) to 4G , and AB ( Hypothesis ) to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the ...
Σελίδα 11
... greater than the other . Let AB be the greater , and from it cut off ( I. 3. ) DB equal to AC , the less , and join DC . Therefore because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , 1. The two sides DB , BC ...
... greater than the other . Let AB be the greater , and from it cut off ( I. 3. ) DB equal to AC , the less , and join DC . Therefore because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , 1. The two sides DB , BC ...
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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