The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 36
... parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts . N ... parallelogram , of which BC is a diameter : the opposite sides and angles of the figure shall be equal to one ...
... parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts . N ... parallelogram , of which BC is a diameter : the opposite sides and angles of the figure shall be equal to one ...
Page 37
... parallelogram ABCD figures . shall be equal to the parallelogram EBCF . 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 each of the paral- B ...
... parallelogram ABCD figures . shall be equal to the parallelogram EBCF . 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 each of the paral- B ...
Page 38
... parallelogram ABCD is equal to the parallelogram EBCF . Therefore parallelograms upon the same base , & c . Q. E. D. + i Ax . PROP . XXXVI . THEOR . DE H Parallelograms upon equal bases , and between the same parallels , are equal to ...
... parallelogram ABCD is equal to the parallelogram EBCF . Therefore parallelograms upon the same base , & c . Q. E. D. + i Ax . PROP . XXXVI . THEOR . DE H Parallelograms upon equal bases , and between the same parallels , are equal to ...
Page 39
... parallelogram : + Def . and EBCA is equal to DBCF , because they 35. L are upon the same base BC , and between the same parallels BC , EF ; and the triangle ABC is the half of the parallelogram EBCA , because the diameter AB bisects it ...
... parallelogram : + Def . and EBCA is equal to DBCF , because they 35. L are upon the same base BC , and between the same parallels BC , EF ; and the triangle ABC is the half of the parallelogram EBCA , because the diameter AB bisects it ...
Page 40
... parallelogram DEFH , because the diameter DF bisects it : but the halves of * 7 Ax . equal things are equal : therefore the triangle ABC is equal to the triangle DEF . Wherefore triangles , & c . Q E. D. PROP . XXXIX . THEOR . Equal ...
... parallelogram DEFH , because the diameter DF bisects it : but the halves of * 7 Ax . equal things are equal : therefore the triangle ABC is equal to the triangle DEF . Wherefore triangles , & c . Q E. D. PROP . XXXIX . THEOR . Equal ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole