The Element of Geometry |
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To draw a straight line from one point to another , may be called joining the points . XIX . Two magnitudes , which being compared exactly fill the same space , may be said to coincide . XX .
To draw a straight line from one point to another , may be called joining the points . XIX . Two magnitudes , which being compared exactly fill the same space , may be said to coincide . XX .
Seite 6
To draw a straight line from one point to another , may be called joining the points . XIX . Two magnitudes , which being compared exactly fill the same space , may be said to coincide . XX .
To draw a straight line from one point to another , may be called joining the points . XIX . Two magnitudes , which being compared exactly fill the same space , may be said to coincide . XX .
Seite 14
AC , disse XB , AC , be produced to D and E , the angle ' s fi tai to ACB , and the angle CBD to the angle BCE . und Bl ? tune any point F , and make AG equal to AF , and join BG , CI . Because AF is equal to AG , and AB to AC , the two ...
AC , disse XB , AC , be produced to D and E , the angle ' s fi tai to ACB , and the angle CBD to the angle BCE . und Bl ? tune any point F , and make AG equal to AF , and join BG , CI . Because AF is equal to AG , and AB to AC , the two ...
Seite 15
equal to AC , one of them is greater than the other ; let AB be the greater , and from it cut off DỄ equal to AC the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both ...
equal to AC , one of them is greater than the other ; let AB be the greater , and from it cut off DỄ equal to AC the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both ...
Seite 16
AF greater than half AB , describe the arc DFE ; from B , with the same radius , describe the arc DGE , intersecting DFE in D , E , and join DE , intersecting AB at C ; AB is bisected at C. Join AD , BD , BE , AE .
AF greater than half AB , describe the arc DFE ; from B , with the same radius , describe the arc DGE , intersecting DFE in D , E , and join DE , intersecting AB at C ; AB is bisected at C. Join AD , BD , BE , AE .
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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
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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...