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, 1851 - 317 σελίδες |
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Σελίδα 5
... common and perfectly well understood . 4. An Axiom , or Maxim , is a self - evident proposition , requiring no forinal demonstration to prove the truth of it ; but is received and assented to as soon as mentioned . Such as , the whole ...
... common and perfectly well understood . 4. An Axiom , or Maxim , is a self - evident proposition , requiring no forinal demonstration to prove the truth of it ; but is received and assented to as soon as mentioned . Such as , the whole ...
Σελίδα 8
... common segment ; that is , they cannot coincide " in part , without coinciding altogether . " 66 4. A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the intersections of ...
... common segment ; that is , they cannot coincide " in part , without coinciding altogether . " 66 4. A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the intersections of ...
Σελίδα 15
... 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 triangle DBC is equal to that of ...
... 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 triangle DBC is equal to that of ...
Σελίδα 17
... common to the two triangles ACD , BCD : the two sides AC , CD , are equal to the two BC , CD , each to each ; but the angle ACD is also equal to the an- gle BCD ; therefore the base AD is equal to the base ( 4. 1. ) DB , and the ...
... common to the two triangles ACD , BCD : the two sides AC , CD , are equal to the two BC , CD , each to each ; but the angle ACD is also equal to the an- gle BCD ; therefore the base AD is equal to the base ( 4. 1. ) DB , and the ...
Σελίδα 18
... common to the two triangles DCF , ECF , the two sides DC , CF are equal to the two EC , CF , each to each ; but the base DF is also equal to the base EF ; therefore the angle DCF is equal ( 8. 1. ) to the angle ECF ; and they are ...
... common to the two triangles DCF , ECF , the two sides DC , CF are equal to the two EC , CF , each to each ; but the base DF is also equal to the base EF ; therefore the angle DCF is equal ( 8. 1. ) to the angle ECF ; and they are ...
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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