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 TrigonometryLippincott, Grambo & Company, 1854 - 317 σελίδες |
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Σελίδα 11
... equal , nor its angles right angles . 29. All other four sided figures besides these , are called trapeziums . 30 ... equal to the same thing are equal to one another . 2. If equals be added to equals , the wholes are equal . 3. If ...
... equal , nor its angles right angles . 29. All other four sided figures besides these , are called trapeziums . 30 ... equal to the same thing are equal to one another . 2. If equals be added to equals , the wholes are equal . 3. If ...
Σελίδα 12
... equal C D A B E ( 11. Definition ) to AB ; and because the point B is the centre of the cir- cle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are ...
... equal C D A B E ( 11. Definition ) to AB ; and because the point B is the centre of the cir- cle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are ...
Σελίδα 13
... equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . PROP . III . PROB . From the greater of two given ...
... equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . PROP . III . PROB . From the greater of two given ...
Σελίδα 14
... equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF cor . def . 3. ) , and ...
... equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF cor . def . 3. ) , and ...
Σελίδα 15
... equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal to the side AC . For , if AB be not ...
... equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal to the side AC . For , if AB be not ...
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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 Let the straight 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