The Element of Geometry |
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Seite 15
for the same reason , in the triangle ACG the angle CAG is equal to the angle CGA ; and therefore , the two angles BAG and A D B F CAG , or BAC , are equal to the two angles BGA and CGA , or BGC ; then the triangles ABC , GBC have the ...
for the same reason , in the triangle ACG the angle CAG is equal to the angle CGA ; and therefore , the two angles BAG and A D B F CAG , or BAC , are equal to the two angles BGA and CGA , or BGC ; then the triangles ABC , GBC have the ...
Seite 23
For the same reason , the angles GHF and GHE are together equal to two right angles ; take away the equal angles AGD and GHF , and the remainder AGC is equal to the remainder GHE : and because AGC and DGH are vertical angles , they are ...
For the same reason , the angles GHF and GHE are together equal to two right angles ; take away the equal angles AGD and GHF , and the remainder AGC is equal to the remainder GHE : and because AGC and DGH are vertical angles , they are ...
Seite 32
But the straight line AD , passing through the point A , is also parallel to BC ; and therefore AD coincides with AF : for the same reason EF coincides with AF . And because ABCD is a parallelogram , AD is equal to BC ( 9.2 . ) .
But the straight line AD , passing through the point A , is also parallel to BC ; and therefore AD coincides with AF : for the same reason EF coincides with AF . And because ABCD is a parallelogram , AD is equal to BC ( 9.2 . ) .
Seite 34
with AG : for the same reason , AB and AH are in the same straight line ; and because the angle DBC is equal to the angle FBA , each of them being a right angle ( Def . 5. 2. ) , add to each the angle ABC , and the whole angle DBĂ is ...
with AG : for the same reason , AB and AH are in the same straight line ; and because the angle DBC is equal to the angle FBA , each of them being a right angle ( Def . 5. 2. ) , add to each the angle ABC , and the whole angle DBĂ is ...
Seite 35
to the triangle ADC ; and because AEKH is a parallelogram , the diagonal of which B G C is AK , the triangle AEK is equal to the triangle AHK ; for the same reason , the triangle KGC is equal to the triangle KFC ; then , because the ...
to the triangle ADC ; and because AEKH is a parallelogram , the diagonal of which B G C is AK , the triangle AEK is equal to the triangle AHK ; for the same reason , the triangle KGC is equal to the triangle KFC ; then , because the ...
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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 |