Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
From inside the book
Results 1-5 of 12
Page 32
... angles together are less than two right angles . A Produce BC to D ; and be- cause ACD is the exterior angle of the triangle ABC , ACD is greater ( 16. 1. ) then the interior and opposite angle ABC ; to each of these add the angle ACB ...
... angles together are less than two right angles . A Produce BC to D ; and be- cause ACD is the exterior angle of the triangle ABC , ACD is greater ( 16. 1. ) then the interior and opposite angle ABC ; to each of these add the angle ACB ...
Page 38
... angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle BCG is equal to the ...
... angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle BCG is equal to the ...
Page 39
... angle equal to the interior and opposite upon the same side of the line ; or makes the interior angles upon the same side together equal to two right angles ; the two straight lines are parallel to one another . Let the straight line EF ...
... angle equal to the interior and opposite upon the same side of the line ; or makes the interior angles upon the same side together equal to two right angles ; the two straight lines are parallel to one another . Let the straight line EF ...
Page 51
... angle now the opposite angles of parallelograms are equal ( 34. 1. ) ; therefore each of the opposite angles ABE , BED is a right an- gle ; wherefore the figure ADEB is rect- D E A B angular , and it has been demonstrated that it is ...
... angle now the opposite angles of parallelograms are equal ( 34. 1. ) ; therefore each of the opposite angles ABE , BED is a right an- gle ; wherefore the figure ADEB is rect- D E A B angular , and it has been demonstrated that it is ...
Page 59
... angle : And because the angle GEF is half a right angle , and EGF a right angle , for it is equal ( 29. 1. ) . to the interior and opposite angle ECB , theremaining angle EFG is half a right A E G F CD B angle ; therefore the angle GEF is ...
... angle : And because the angle GEF is half a right angle , and EGF a right angle , for it is equal ( 29. 1. ) . to the interior and opposite angle ECB , theremaining angle EFG is half a right A E G F CD B angle ; therefore the angle GEF is ...
Other editions - View all
Common terms and phrases
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line BD THEOR third touches the circle triangle ABC triangle DEF wherefore