The Element of Geometry |
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Seite 33
E To describe a square upon a given straight line . Let AB be the given straight line ; it is required to describe a square From the point A , draw AC at right angles ( 9. 1. ) to AB , and make AD equal to AB ; and through the point D ...
E To describe a square upon a given straight line . Let AB be the given straight line ; it is required to describe a square From the point A , draw AC at right angles ( 9. 1. ) to AB , and make AD equal to AB ; and through the point D ...
Seite 34
... the adjacent angles equal to two right angles ; therefore AC is in the same straight line ( 2. 1. ) ... and the squares BG , CH upon AB , AC ; therefore the square upon the side BC , is equal to the squares upon the sides AB , AC .
... the adjacent angles equal to two right angles ; therefore AC is in the same straight line ( 2. 1. ) ... and the squares BG , CH upon AB , AC ; therefore the square upon the side BC , is equal to the squares upon the sides AB , AC .
Seite 35
A ABC , be equal to the squares upon the other sides AB , AC , the angle BAC is a right angle . ... to AC , and make AD equal to AB , and join ČD ; then , because AD is equal to AB , D the square of AD is equal to the square of AB ...
A ABC , be equal to the squares upon the other sides AB , AC , the angle BAC is a right angle . ... to AC , and make AD equal to AB , and join ČD ; then , because AD is equal to AB , D the square of AD is equal to the square of AB ...
Seite 36
Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares of AC , CB , and to twice the rectangle contained by AC , CB . Upon AB describe ( 16. 2. ) the square ADEB , and join BD ...
Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares of AC , CB , and to twice the rectangle contained by AC , CB . Upon AB describe ( 16. 2. ) the square ADEB , and join BD ...
Seite 37
the square CEFB , join BE , and through D draw ( 4. 2. ) DHG parallel to CE or BF ; and through H ... to AL , because AC is equal to CB ; therefore also AL is equal to DF ; С B to each of these , add CH , and the whole AH is equal to DF ...
the square CEFB , join BE , and through D draw ( 4. 2. ) DHG parallel to CE or BF ; and through H ... to AL , because AC is equal to CB ; therefore also AL is equal to DF ; С B to each of these , add CH , and the whole AH is equal to DF ...
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The Element of Geometry (Classic Reprint) Formerly Chairman Department of Immunology John Playfair,John Playfair Keine Leseprobe verfügbar - 2017 |
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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 |