The First Six Books with NotesR. Milliken, 1822 - 179 pages |
From inside the book
Results 6-10 of 24
Page 48
... fall from the opposite angle . The square of BA is equal to the sum of the squares ( 1 ) Prop.47 of AD and DB ( 1 ) , but the square of DB is equal to the squaresof DC and CB , together with double the rect- ( 2 ) Prop 4. angle under DC ...
... fall from the opposite angle . The square of BA is equal to the sum of the squares ( 1 ) Prop.47 of AD and DB ( 1 ) , but the square of DB is equal to the squaresof DC and CB , together with double the rect- ( 2 ) Prop 4. angle under DC ...
Page 49
... fall from the opposite angle . The squares of AC and CF are equal to twice the rectangle under AC and CF , together with the square of AF ( 1 ) , and , if the square of the perpen- ( 1 ) Prop . 7 . dicular BF be added to both , the ...
... fall from the opposite angle . The squares of AC and CF are equal to twice the rectangle under AC and CF , together with the square of AF ( 1 ) , and , if the square of the perpen- ( 1 ) Prop . 7 . dicular BF be added to both , the ...
Page 52
... falls , is said to be farther from the centre . 6. A segment of a circle is the figure contained by a right line , and the part of the circumference it cuts . off . 7. An angle in a segment is the angle contained by two right lines ...
... falls , is said to be farther from the centre . 6. A segment of a circle is the figure contained by a right line , and the part of the circumference it cuts . off . 7. An angle in a segment is the angle contained by two right lines ...
Page 53
... falls within the circle . For , if it be possible , let AEB be a right line in which the point E is without the circle , and draw DA , DE , and DB . ( 1 ) Def . 15 . ( 2 ) Prop . Because in the triangle ADB , the sides DA and DB B. 1 ...
... falls within the circle . For , if it be possible , let AEB be a right line in which the point E is without the circle , and draw DA , DE , and DB . ( 1 ) Def . 15 . ( 2 ) Prop . Because in the triangle ADB , the sides DA and DB B. 1 ...
Page 54
... falls within a circle . PROP . III . THEOR . If a right line ( BL ) drawn through the centre of a circle bisect a right line ( CF ) which does not pass through the centre , it is perpendicular to it . And if it cut it at right angles ...
... falls within a circle . PROP . III . THEOR . If a right line ( BL ) drawn through the centre of a circle bisect a right line ( CF ) which does not pass through the centre , it is perpendicular to it . And if it cut it at right angles ...
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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.