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 páginas |
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Página 33
... figure , of which the opposite sides are parallel ; and the 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 ...
... figure , of which the opposite sides are parallel ; and the 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 ...
Página 36
... figures EBCA , DBCF , is a parallelogram ; 2. EBCA is equal to DBCF , because they are upon the same base BC , and between the same parallels BC , EF ; and ( I. 34. ) 3. The triangle ABC is the half of the parallelogram EBCA , because ...
... figures EBCA , DBCF , is a parallelogram ; 2. EBCA is equal to DBCF , because they are upon the same base BC , and between the same parallels BC , EF ; and ( I. 34. ) 3. The triangle ABC is the half of the parallelogram EBCA , because ...
Página 37
... figures GBCA , DEFH , is a parallelogram ; 2. GBCA , DEFH , are equal to one another , because they are upon equal bases BC , EF , and between the same parallels BF , GH ; and ( I. 34. ) 3. The triangle ABC is the half of the ...
... figures GBCA , DEFH , is a parallelogram ; 2. GBCA , DEFH , are equal to one another , because they are upon equal bases BC , EF , and between the same parallels BF , GH ; and ( I. 34. ) 3. The triangle ABC is the half of the ...
Página 40
... figure ABCD , which are therefore called the complements . The complement BK is equal to the complement KD . A H K 1 . B G Because ABCD is a parallelogram , and AC its diameter , ( I. 34. ) The triangle ABC is equal to the triangle ADC ...
... figure ABCD , which are therefore called the complements . The complement BK is equal to the complement KD . A H K 1 . B G Because ABCD is a parallelogram , and AC its diameter , ( I. 34. ) The triangle ABC is equal to the triangle ADC ...
Página 42
... figure , and E the given rectilineal angle . It is required to describe a parallelogram equal to ABCD , and having ... figure FKML shall be the parallelogram required . F G L B CK H M Because the angle E is equal to each of the angles ...
... figure , and E the given rectilineal angle . It is required to describe a parallelogram equal to ABCD , and having ... figure FKML shall be the parallelogram required . F G L B CK H M Because the angle E is equal to each of the angles ...
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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