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., En¾ |
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Seite 216
... the cylinder described by twice the rectan gle BD , that is , to two - thirds of the circumscribing cylinder . END OF THE SUPPLEMENT TO THE ELEMENTS . 9. The sine , tangent , or secant of the 216 SUPPLEMENT TO THE ELEMENTS , & c .
... the cylinder described by twice the rectan gle BD , that is , to two - thirds of the circumscribing cylinder . END OF THE SUPPLEMENT TO THE ELEMENTS . 9. The sine , tangent , or secant of the 216 SUPPLEMENT TO THE ELEMENTS , & c .
Seite 219
I K AC , perpendicular to the diameter passing through the other extremity A , is called the Sine of the arc AC , or of the angle ABC , of which AC is the measure . L E B D COR 1. The sine of a quadrant , or of a right angle , is equal ...
I K AC , perpendicular to the diameter passing through the other extremity A , is called the Sine of the arc AC , or of the angle ABC , of which AC is the measure . L E B D COR 1. The sine of a quadrant , or of a right angle , is equal ...
Seite 220
The sine , tangent , or secant of the complement of any angle is called the Cosine , Cotangent , or Cosecant of that angle . Thus , let CL or DB , which is equal to CL , be the sine of the angle CBH ; HK the tangent , and BK the secant ...
The sine , tangent , or secant of the complement of any angle is called the Cosine , Cotangent , or Cosecant of that angle . Thus , let CL or DB , which is equal to CL , be the sine of the angle CBH ; HK the tangent , and BK the secant ...
Seite 221
Therefore , 1B CB : BA :: CD : DF ; but CD is the radius , and DF the sine of the angle C , ( Def . 4. ) ; therefore CB : BA :: R : sin . C. Also , because EG touches the circle in E , CEG is a right angle , and therefore equal to the ...
Therefore , 1B CB : BA :: CD : DF ; but CD is the radius , and DF the sine of the angle C , ( Def . 4. ) ; therefore CB : BA :: R : sin . C. Also , because EG touches the circle in E , CEG is a right angle , and therefore equal to the ...
Seite 222
E B K G E LH Now , since EL from the centre is perpendicular to CD , it bisects the line CD in L and the arc CAD in A : DL is therefore equal to LC , or to the sine of the arc AC ; and BH or LK being the sine of AB , DK is the sum of ...
E B K G E LH Now , since EL from the centre is perpendicular to CD , it bisects the line CD in L and the arc CAD in A : DL is therefore equal to LC , or to the sine of the arc AC ; and BH or LK being the sine of AB , DK is the sum of ...
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ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremity fall fore four given given straight line greater half Hence inscribed interior join less Let ABC likewise magnitudes manner mean meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides sine solid square straight line taken tangent THEOR third touch triangle ABC wherefore whole
Beliebte Passagen
Seite 7 - 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 116 - 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 68 - 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 88 - 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 9 - 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 284 - 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 271 - 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 137 - ... 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 11 - If two triangles have two sides of the one equal to two sides of the...
Seite 30 - 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.
Bibliografische Informationen
| Titel | 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., En¾ Dean's stereotype edition |
| Autor/in | John Playfair |
| Verlag | J.B. Lippincott & Company, 1855 |
| Original von | New York Public Library |
| Digitalisiert | 21. Juni 2006 |
| Länge | 317 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |