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 TrigonometryW. E. Dean, 1840 - 317 σελίδες |
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Σελίδα 5
... prove the truth of it ; but is received and assented to as soon as mentioned . Such as , the whole of any thing is greater ... proved . Thus , when it is said that the sum of the three angles of any plane tri- angle is equal to two right ...
... prove the truth of it ; but is received and assented to as soon as mentioned . Such as , the whole of any thing is greater ... proved . Thus , when it is said that the sum of the three angles of any plane tri- angle is equal to two right ...
Σελίδα 6
... proving that some absurdity would necessarily follow if the proposition advanced were false . This is sometimes called Reductio ad Absurdum ; because it shows the absurdity and falsehood of all suppositions contrary to that contained in ...
... proving that some absurdity would necessarily follow if the proposition advanced were false . This is sometimes called Reductio ad Absurdum ; because it shows the absurdity and falsehood of all suppositions contrary to that contained in ...
Σελίδα 12
... proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same are equal to one another , ( 1. Axiom ) ; there- fore CA is equal to CB ; wherefore CA , AB , CB are equal to one ...
... proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same are equal to one another , ( 1. Axiom ) ; there- fore CA is equal to CB ; wherefore CA , AB , CB are equal to one ...
Σελίδα 14
... proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the tri- angles BFC , CGB are equal ( 4. 1. ) , and their remaining angles ...
... proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the tri- angles BFC , CGB are equal ( 4. 1. ) , and their remaining angles ...
Σελίδα 15
... proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to ...
... proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional 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 touches the circle triangle ABC triangle DEF wherefore