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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 20
... angle EGB is equal to the angle GHD , and also ( 8. 1. ) to the angle AGH , the angle AGH is equal to the angle GHD ... exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the ...
... angle EGB is equal to the angle GHD , and also ( 8. 1. ) to the angle AGH , the angle AGH is equal to the angle GHD ... exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the ...
Página 22
... angle GHF . Again , because the straight line GK cuts the parallel straight lines EF , CD , the angle GHF is equal ... exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every trian- gle ...
... angle GHF . Again , because the straight line GK cuts the parallel straight lines EF , CD , the angle GHF is equal ... exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every trian- gle ...
Página 23
... exterior an- gle ECD is equal to the interior and opposite angle ABC , but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole ex- terior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these ...
... exterior an- gle ECD is equal to the interior and opposite angle ABC , but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole ex- terior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these ...
Página 24
... angles as the figure has sides , wanting four . COR . 1. All the exterior angles of any rectilineal figure are together equal to four right angles . Because every interior an- gle ABC , with its adjacent exterior ABD , is equal ( 6. 1 ...
... angles as the figure has sides , wanting four . COR . 1. All the exterior angles of any rectilineal figure are together equal to four right angles . Because every interior an- gle ABC , with its adjacent exterior ABD , is equal ( 6. 1 ...
Página 46
... exterior angle BGC is equal ( 21. 1. ) to the interior and opposite angle ADB ; but ADB is equal ( 3. 1. ) to the angle ABD , because BA is equal to AD , be- ing sides of a square ; wherefore the angle CGB is equal to the angle GBC ...
... exterior angle BGC is equal ( 21. 1. ) to the interior and opposite angle ADB ; but ADB is equal ( 3. 1. ) to the angle ABD , because BA is equal to AD , be- ing sides of a square ; wherefore the angle CGB is equal to the angle GBC ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore