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 50
... falls upon them , ( I. 29. ) 1. The exterior angle BGC is equal to the interior and opposite angle ADB ; but ( I. 5. ) 2. ADB is equal to the angle ABD , because BA is equal to AD , being sides of a square ; wherefore 3. The angle CGB ...
... falls upon them , ( I. 29. ) 1. The exterior angle BGC is equal to the interior and opposite angle ADB ; but ( I. 5. ) 2. ADB is equal to the angle ABD , because BA is equal to AD , being sides of a square ; wherefore 3. The angle CGB ...
Σελίδα 60
... falls , and the straight line intercepted without the triangle , between the perpendicular and the obtuse angle . Let ABC be an obtuse - angled triangle , having the obtuse angle ACB ; and from the point A let AD be drawn ( I. 12 ...
... falls , and the straight line intercepted without the triangle , between the perpendicular and the obtuse angle . Let ABC be an obtuse - angled triangle , having the obtuse angle ACB ; and from the point A let AD be drawn ( I. 12 ...
Σελίδα 61
... fall upon it from the opposite angle , and the acute angle . Let ABC be any triangle , and the angle at B one of its acute angles ; and upon BC , one of the sides containing it , let fall ( I. 12. ) the perpen- dicular AD from the ...
... fall upon it from the opposite angle , and the acute angle . Let ABC be any triangle , and the angle at B one of its acute angles ; and upon BC , one of the sides containing it , let fall ( I. 12. ) the perpen- dicular AD from the ...
Σελίδα 65
... falls is said to be farther from the centre . VI . A segment of a circle is the figure contained by a straight line and the circumference it cuts off . VII . " The angle of a segment is that which is contained by the straight line and ...
... falls is said to be farther from the centre . VI . A segment of a circle is the figure contained by a straight line and the circumference it cuts off . VII . " The angle of a segment is that which is contained by the straight line and ...
Σελίδα 66
... bisects the other . PROP . II . THEOREM . If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A , B 66 EUCLID'S ELEMENTS .
... bisects the other . PROP . II . THEOREM . If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A , B 66 EUCLID'S ELEMENTS .
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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