The Element of Geometry |
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Seite 43
IV . of a circle contained by a straight line and the circumference which it cuts off , may be called a segment of a circle , and the straight line may be called the base of the segment . The part V. The angle contained by two straight ...
IV . of a circle contained by a straight line and the circumference which it cuts off , may be called a segment of a circle , and the straight line may be called the base of the segment . The part V. The angle contained by two straight ...
Seite 44
V. The angle contained by two straight lines drawn from any point in the circumference of the segment , to the extremities of the base of the segment , may be called the angle in a segment . VI . An angle may be said to stand on the ...
V. The angle contained by two straight lines drawn from any point in the circumference of the segment , to the extremities of the base of the segment , may be called the angle in a segment . VI . An angle may be said to stand on the ...
Seite 45
the circumference DAB will fall upon the circumference BCD , and the A segment DAB will be equivalent to the segment BCD . Therefore , the diameter divides the circle into two equivalent parts . Which was to be proved . C D PROP . III .
the circumference DAB will fall upon the circumference BCD , and the A segment DAB will be equivalent to the segment BCD . Therefore , the diameter divides the circle into two equivalent parts . Which was to be proved . C D PROP . III .
Seite 52
The angles in the same segment of a circle are equal to one another . ... Take F the centre of the circle ABCD ; F and first , let the segment BAED be greater than a semicircle , and join BF , FD ; and because the angle BFD is at the ...
The angles in the same segment of a circle are equal to one another . ... Take F the centre of the circle ABCD ; F and first , let the segment BAED be greater than a semicircle , and join BF , FD ; and because the angle BFD is at the ...
Seite 53
a But , if the segment BAD be not greater than a semicircle , let BAD , BED be angles in it ; these also are equal to one another : draw AF to the centre , and produce B it to C , and join CE : therefore the segment BADC is greater than ...
a But , if the segment BAD be not greater than a semicircle , let BAD , BED be angles in it ; these also are equal to one another : draw AF to the centre , and produce B it to C , and join CE : therefore the segment BADC is greater than ...
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The Element of Geometry (Classic Reprint) Formerly Chairman Department of Immunology John Playfair,John Playfair Keine Leseprobe verfügbar - 2017 |
Häufige Begriffe und Wortgruppen
AC is equal angle ABC angle ACB angle BAC angled triangle angles equal base bisect called centre circle circle ABCD circumference coincide common described diameter difference direction distance divided double draw drawn equal angles equiangular equivalent extremity fall figure fore four given straight line greater half join length less Let ABC likewise mean meet parallel parallelogram pass perpendicular plane polygon produced PROP proportional proved Q. E. D. PROP quantities radius ratio reason rectangle contained rectilineal figure remaining angle right angles segment side AC sides similar sine space square of AC tangent THEOR third triangle ABC twice the rectangle wherefore whole
Beliebte Passagen
Seite 25 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Seite 13 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line E iR.
Seite 4 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Seite 29 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Seite 90 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Seite 87 - ... magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Seite 1 - If two triangles have two sides of the one equal to two sides of the...
Seite 13 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Seite 64 - 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 19 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Bibliografische Informationen
| Titel | The Element of Geometry |
| Autor/in | John Playfair |
| Verlag | W.E. Dean, 1836 |
| Original von | New York Public Library |
| Digitalisiert | 21. Juni 2006 |
| Länge | 114 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |