Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement ... to which are Added, Elements of Plane and Sphericale Trigonometry ... From the Last London Ed., EnlJ.B. Lippincott & Company, 1855 - 317 Seiten |
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Seite 17
... construction , each of the halves BAF , CAF , may be divi ded into two equal parts ; and thus , by successive subdivisions , a given an- gle may be divided into four equal parts , into eight , into sixteen , and so on . PROP . X. PROB ...
... construction , each of the halves BAF , CAF , may be divi ded into two equal parts ; and thus , by successive subdivisions , a given an- gle may be divided into four equal parts , into eight , into sixteen , and so on . PROP . X. PROB ...
Seite 37
... construction will apply to the problem : to make a triangle equivalent to a given rectangle . PROP . XLIII . THEOR . The complements of the parallelograms which are about the diameter of any parallelogram , are equal to one another ...
... construction will apply to the problem : to make a triangle equivalent to a given rectangle . PROP . XLIII . THEOR . The complements of the parallelograms which are about the diameter of any parallelogram , are equal to one another ...
Seite 45
... construction will apply : for , mak ing BCA equal to the given angle , and AC equal to the adjacent side ; then , from A as centre , with a radius equal to the other given side , describe an arc , cutting CB in B ; draw AB , and CAB ...
... construction will apply : for , mak ing BCA equal to the given angle , and AC equal to the adjacent side ; then , from A as centre , with a radius equal to the other given side , describe an arc , cutting CB in B ; draw AB , and CAB ...
Seite 46
... construction which reduces two of them to one , will reduce three of them to two , and these two to one , and so of others . PROP . I. PROB . To find the side of a square equivalent to the difference of two given squares . Draw , as in ...
... construction which reduces two of them to one , will reduce three of them to two , and these two to one , and so of others . PROP . I. PROB . To find the side of a square equivalent to the difference of two given squares . Draw , as in ...
Seite 64
... construction being made , because the radii EA , FB are equal to one another , the angle EAF is equal ( 5. 1. ) to the angle EBF ; and the right angle AFE is equal to the right angle BFE : Therefore , in the two triangles EAF , EBF ...
... construction being made , because the radii EA , FB are equal to one another , the angle EAF is equal ( 5. 1. ) to the angle EBF ; and the right angle AFE is equal to the right angle BFE : Therefore , in the two triangles EAF , EBF ...
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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 coincide cosine cylinder definition demonstrated described diameter divided draw 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 magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB produced PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
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Seite 3 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Seite 122 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 74 - The angle in a semicircle is a right angle: the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Seite 44 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Seite 5 - Let it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Seite 290 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 277 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 143 - ... cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Seite 7 - If two triangles have two sides of the one equal to two sides of the...
Seite 26 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.