The Element of Geometry |
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Seite 21
A quadrangle , whose opposite sides are parallel , may be called a parallelogram . IV . A parallelogram , whose angles are right angles , may be called a rectangle . 0 V. A rectangle , whose sides are equal , may be called a square .
A quadrangle , whose opposite sides are parallel , may be called a parallelogram . IV . A parallelogram , whose angles are right angles , may be called a rectangle . 0 V. A rectangle , whose sides are equal , may be called a square .
Seite 22
A quadrangle that is not a parallelogram , may be called a trapezium . IX . A straight line joining the two opposite angles of a parallelogram , may be called a diagonal . X. Let ABCD be a parallelogram , AC A H D a diagonal .
A quadrangle that is not a parallelogram , may be called a trapezium . IX . A straight line joining the two opposite angles of a parallelogram , may be called a diagonal . X. Let ABCD be a parallelogram , AC A H D a diagonal .
Seite 28
The opposite sides and angles of a parallelogram are equal . In the quadrangle ABDC , lct AB be parallel to CD , and AC to BD . AB is equal to CD , and AC to BD . Join BC . Because AB is parallel to CD , and BC meets them ...
The opposite sides and angles of a parallelogram are equal . In the quadrangle ABDC , lct AB be parallel to CD , and AC to BD . AB is equal to CD , and AC to BD . Join BC . Because AB is parallel to CD , and BC meets them ...
Seite 29
Because the triangles ABC , BCD are equivalent , as proved above ; therefore the diagonal bisects the parallelogram . PROP . X. THEOR . Two straight lines which are at the same distance at each extremity , are parallel .
Because the triangles ABC , BCD are equivalent , as proved above ; therefore the diagonal bisects the parallelogram . PROP . X. THEOR . Two straight lines which are at the same distance at each extremity , are parallel .
Seite 30
AC is parallel to BD , and ABDC is a parallelogram ; and therefore AC is equal ( 9. 2. ) to BD . Therefore the perpendiculars between parallel lines are equal . Which was to be proved . Cor . If parallel lines are produced indefinitely ...
AC is parallel to BD , and ABDC is a parallelogram ; and therefore AC is equal ( 9. 2. ) to BD . Therefore the perpendiculars between parallel lines are equal . Which was to be proved . Cor . If parallel lines are produced indefinitely ...
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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 |