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 1
... common and perfectly well understood . 4. An Axiom , or Maxim , is a self - evident proposition , requiring no formal demonstration to prove the truth of it ; but is received and assented to as soon as mentioned . Such as , the whole of ...
... common and perfectly well understood . 4. An Axiom , or Maxim , is a self - evident proposition , requiring no formal demonstration to prove the truth of it ; but is received and assented to as soon as mentioned . Such as , the whole of ...
Página 4
... common segment ; that is , they cannot coincide " in part , without coinciding altogether . " 4. A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the intersections of one ...
... common segment ; that is , they cannot coincide " in part , without coinciding altogether . " 4. A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the intersections of one ...
Página 10
... common ; therefore , these two triangles are identical , or equal in all respects , ( Theor . 1. ) ; and conse- quently , the angle A equal to the angle B. A COR . Every equilateral triangle is also equiangular . SCHOLIUM . D B The ...
... common ; therefore , these two triangles are identical , or equal in all respects , ( Theor . 1. ) ; and conse- quently , the angle A equal to the angle B. A COR . Every equilateral triangle is also equiangular . SCHOLIUM . D B The ...
Página 11
... common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the base DC is equal to the base AB , and the area of the trian- gle DBC is equal to that ...
... common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore the base DC is equal to the base AB , and the area of the trian- gle DBC is equal to that ...
Página 18
... common to the two tri- angles ABC , ABE , and the contained angles ABC and ABE equal ; the two triangles must be equal ( Th . 1. ) ; hence AE , AC are equal . D C B E Finally , the angle ACB being acute , as before , the adjacent angle ...
... common to the two tri- angles ABC , ABE , and the contained angles ABC and ABE equal ; the two triangles must be equal ( Th . 1. ) ; hence AE , AC are equal . D C B E Finally , the angle ACB being acute , as before , the adjacent angle ...
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Términos y frases comunes
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