The Element of Geometry |
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Page 11
... fall as GD , then the angles ACD , BCD will coincide with the angles EGD and DGF . Because the angles EGD and DGF are composed of the three angles EGD , DGH , FGH , and the angles EGH , FGH also composed of the same three angles , EGD ...
... fall as GD , then the angles ACD , BCD will coincide with the angles EGD and DGF . Because the angles EGD and DGF are composed of the three angles EGD , DGH , FGH , and the angles EGH , FGH also composed of the same three angles , EGD ...
Page 22
... perpendicular drawn from an angle of a triangle or parallelogram , to the base or base produced , may be called the altitude of the tri- angle , or parallelogram . PROPOSITION I. THEOREM . If a straight line falling on 22 THE ELEMENT.
... perpendicular drawn from an angle of a triangle or parallelogram , to the base or base produced , may be called the altitude of the tri- angle , or parallelogram . PROPOSITION I. THEOREM . If a straight line falling on 22 THE ELEMENT.
Page 23
... falling on two other straight lines in the same plane , makes the corresponding angles equal , any other straight line falling on those two straight lines , will also make the corresponding angles equal . Let the straight line EF fall ...
... falling on two other straight lines in the same plane , makes the corresponding angles equal , any other straight line falling on those two straight lines , will also make the corresponding angles equal . Let the straight line EF fall ...
Page 24
... fall on two parallel lines , it makes the corresponding an- gles equal . E A G B Let the straight line EF fall on the two parallel lines AB , CD ; it makes the corresponding angles equal . Because AB is parallel to CD , it is in the ...
... fall on two parallel lines , it makes the corresponding an- gles equal . E A G B Let the straight line EF fall on the two parallel lines AB , CD ; it makes the corresponding angles equal . Because AB is parallel to CD , it is in the ...
Page 25
... , and AC meets them , the cor- responding angles BAC , ACE are equal ( 3. 2. ) . Again , because AB is parallel to CE , and BD falls upon them 4 OF GEOMETRY . BOOK II . 25 if a straight line fall on two parallel lines, ...
... , and AC meets them , the cor- responding angles BAC , ACE are equal ( 3. 2. ) . Again , because AB is parallel to CE , and BD falls upon them 4 OF GEOMETRY . BOOK II . 25 if a straight line fall on two parallel lines, ...
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The Element of Geometry (Classic Reprint) Formerly Chairman Department of Immunology John Playfair,John Playfair No preview available - 2017 |
Common terms and phrases
AB is equal AC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF arc AC base BC bisect called centre circle ABCD circle EFGH coincide described divided drawn duplicate ratio equal 17 equal angles equal circles equal to CD equiangular FGHKL fore four right angles given straight line gnomon greater homologous sides join less Let ABC Let the straight opposite angles parallel parallelogram perpendicular polygon PROB produced Q. E. D. PROP radius rectangle BC rectangle contained rectilineal figure remaining angle right angled triangle secant segment side AC similar sine square of AC straight line AB straight line AC THEOR touches the circle triangle ABC twice the rectangle wherefore whole angle
Popular passages
Page 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.
Page 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.
Page 4 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Page 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...
Page 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.
Page 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.
Page 1 - If two triangles have two sides of the one equal to two sides of the...
Page 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.
Page 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.
Page 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...