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 33
... parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts ... parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another ...
... parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts ... parallelogram , of which BC is a diameter ; the opposite sides and angles of the figure are equal to one another ...
Σελίδα 34
... parallelogram ABCD shall be equal to the parallelogram EBCF . B B AED F B C If the sides AD , DF , of the parallelograms ABCD , DBCF , opposite to the base BC be terminated in the same point D , it is plain that ( I. 34. ) Each of the ...
... parallelogram ABCD shall be equal to the parallelogram EBCF . B B AED F B C If the sides AD , DF , of the parallelograms ABCD , DBCF , opposite to the base BC be terminated in the same point D , it is plain that ( I. 34. ) Each of the ...
Σελίδα 35
... parallelogram ABCD is equal to the parallelogram EBCF . Therefore parallelograms upon the same base , & c . Q.E.D. PROP . XXXVI . - THEOREM . Parallelograms upon equal bases and between the same parallels , are equal to one another ...
... parallelogram ABCD is equal to the parallelogram EBCF . Therefore parallelograms upon the same base , & c . Q.E.D. PROP . XXXVI . - THEOREM . Parallelograms upon equal bases and between the same parallels , are equal to one another ...
Σελίδα 36
... parallelogram EFGH is equal to the same EBCH . Therefore also 6. The parallelogram ABCD is equal to EFGH . Wherefore , parallelograms , & c . Q.E.D. PROP . XXXVII . - THEOREM . Triangles upon the same base and between the same parallels ...
... parallelogram EFGH is equal to the same EBCH . Therefore also 6. The parallelogram ABCD is equal to EFGH . Wherefore , parallelograms , & c . Q.E.D. PROP . XXXVII . - THEOREM . Triangles upon the same base and between the same parallels ...
Σελίδα 37
... 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 parallelogram GBCA , because the ...
... 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 parallelogram GBCA , because the ...
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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