The First Six Books with NotesR. Milliken, 1822 - 179 pages |
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Page 7
... equiangular triangle is also equi- lateral ; for whatever side is taken for the base , the angles adjacent to it are equal , and therefore the sides which subtend them . PROP . VII . THEOR . On the same right line ( AB ) and onthe same ...
... equiangular triangle is also equi- lateral ; for whatever side is taken for the base , the angles adjacent to it are equal , and therefore the sides which subtend them . PROP . VII . THEOR . On the same right line ( AB ) and onthe same ...
Page 78
... equi- angular to a given triangle ( EDF ) . Draw the line GH a tangent to the given circle in any point A at the ... equiangular to a given triangle ( EDF ) . Produce any side DF of the given triangle both ways to G and H , from the ...
... equi- angular to a given triangle ( EDF ) . Draw the line GH a tangent to the given circle in any point A at the ... equiangular to a given triangle ( EDF ) . Produce any side DF of the given triangle both ways to G and H , from the ...
Page 79
... equiangular to the given triangle .. PROP . IV . PROB . In a given triangle ( BAC ) to inscribe a circle . Bisect any two angles B and C by the right lines BD and CD , and from their point of concourse D draw DF perpendicular to any ...
... equiangular to the given triangle .. PROP . IV . PROB . In a given triangle ( BAC ) to inscribe a circle . Bisect any two angles B and C by the right lines BD and CD , and from their point of concourse D draw DF perpendicular to any ...
Page 84
... equiangular pentagon . Construct an isosceles triangle , in which each of the angles at the base shall be double of the angle at the ( 1 ) Prop . 10. vertex ( 1 ) , and inscribe in the given circle a triangle equiangular to it ACE ( 2 ) ...
... equiangular pentagon . Construct an isosceles triangle , in which each of the angles at the base shall be double of the angle at the ( 1 ) Prop . 10. vertex ( 1 ) , and inscribe in the given circle a triangle equiangular to it ACE ( 2 ) ...
Page 85
... equiangular . Cor . 2. An equiangular figure , inscribed in a circle , has its alternate sides equal , as is evident from the equality of the arches which contain equal angles . Schol . Hence if the number of sides be odd , the figure ...
... equiangular . Cor . 2. An equiangular figure , inscribed in a circle , has its alternate sides equal , as is evident from the equality of the arches which contain equal angles . Schol . Hence if the number of sides be odd , the figure ...
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Common terms and phrases
absurd AC and BD AC and CB AC are equal alternate angles angle ABC angle ACD angle BAC angle equal base bisected centre circumference CKMB Constr constructed contained in CD demonstrated double the rectangle double the square equal angles equal sides equal to AC equal to double equi equi-multiples equi-submultiples equiangular Euclid evident fore four magnitudes proportional four right angles given angle given circle given line given right line given triangle half a right Hypoth inscribed less line CD manner mean proportional multiple oftener parallel parallelogram perpendicular point of contact PROB produced Prop proposition radius rectangle under AC right line AB Schol segment side AC similar squares of AC submultiple taken tangent THEOR third tiple triangle ABC vertex
Popular passages
Page 145 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Page 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16.
Page 28 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 22 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 118 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.
Page 146 - A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
Page 168 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Page 3 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another.
Page 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Page 3 - A rhombus is that which has all its sides equal, but its angles are not right angles.