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 37
... triangle ABC , having one of its angles CEF equal to the given angle D. COR . Hence , if the angle D be a right angle , the parallelogram EFGC will be a rectangle , equivalent to the triangle ABC ; and therefore the same construction ...
... triangle ABC , having one of its angles CEF equal to the given angle D. COR . Hence , if the angle D be a right angle , the parallelogram EFGC will be a rectangle , equivalent to the triangle ABC ; and therefore the same construction ...
Seite 38
... triangle may be converted into an equivalent rectangle , having a side of a given length : for , if the angle D be a right angle , and AB the given side , the parallelogram ABML will be a rectangle equiva lent to the triangle C. PROP ...
... triangle may be converted into an equivalent rectangle , having a side of a given length : for , if the angle D be a right angle , and AB the given side , the parallelogram ABML will be a rectangle equiva lent to the triangle C. PROP ...
Seite 46
... triangle will at length be found . COR . Since a triangle may be converted into an equivalent rectangle it follows that any polygon may be reduced to an equivalent rectangle . PROP . H. PROB . To find the side of a square that shall be ...
... triangle will at length be found . COR . Since a triangle may be converted into an equivalent rectangle it follows that any polygon may be reduced to an equivalent rectangle . PROP . H. PROB . To find the side of a square that shall be ...
Seite 46
... rectangle GFKC , having the side FG of a given length , is equal to the given rectangle AEFH ( 43. 1. ) A E H F B G COR . A polygon may be converted into an equivalent rectangle , having one fits sides of a given length . ELEMENTS OF ...
... rectangle GFKC , having the side FG of a given length , is equal to the given rectangle AEFH ( 43. 1. ) A E H F B G COR . A polygon may be converted into an equivalent rectangle , having one fits sides of a given length . ELEMENTS OF ...
Seite 46
... rectangle contained by AD and DC , we shall simply say " the rectangle AD . ĎC , placing a point between the two sides of the " rectangle . " A. In Geometry , the product of two lines means the same thing as their rectangle , and this ...
... rectangle contained by AD and DC , we shall simply say " the rectangle AD . ĎC , placing a point between the two sides of the " rectangle . " A. In Geometry , the product of two lines means the same thing as their rectangle , and this ...
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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
Beliebte Passagen
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.