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 3
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter ...
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter ...
Σελίδα 33
... diameter is the straight line joining two of its opposite angles , Let ACDB be a parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another ; and the diameter BC bisects it . B ...
... diameter is the straight line joining two of its opposite angles , Let ACDB be a parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another ; and the diameter BC bisects it . B ...
Σελίδα 34
... diameter bisects them ; for AB being equal to CD , and BC common , the two AB , BC , are equal to the two DC , CB , each to each ; and the angle ABC has been proved equal to the angle BCD ; therefore ( I. 4. ) 5. The triangle ABC is ...
... diameter bisects them ; for AB being equal to CD , and BC common , the two AB , BC , are equal to the two DC , CB , each to each ; and the angle ABC has been proved equal to the angle BCD ; therefore ( I. 4. ) 5. The triangle ABC is ...
Σελίδα 36
... diameter AB bisects it ; and 4. The triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it . But the halves of equal things are equal ( Ax . 7. ) ; therefore 5. The triangle ABC is equal to the triangle ...
... diameter AB bisects it ; and 4. The triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it . But the halves of equal things are equal ( Ax . 7. ) ; therefore 5. The triangle ABC is equal to the triangle ...
Σελίδα 37
... diameter AB bisects it ; and 4. The triangle DEF is the half of the parallelogram DEH , because the diameter DF bisects it . But the halves of equal things are equal ( Ax . 7. ) ; therefore 5. The triangle ABC is equal to the triangle ...
... diameter AB bisects it ; and 4. The triangle DEF is the half of the parallelogram DEH , because the diameter DF bisects it . But the halves of equal things are equal ( Ax . 7. ) ; therefore 5. The triangle ABC is equal to the triangle ...
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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