The First Six Books with NotesR. Milliken, 1822 - 179 pages |
From inside the book
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Page 34
... rectangle or right angled parallelogram is said to be contained by the two right lines , which contain one of its right angles . ( It is called the rectangle under these two lines . ) 2. In any parallelogram either of the parallelograms ...
... rectangle or right angled parallelogram is said to be contained by the two right lines , which contain one of its right angles . ( It is called the rectangle under these two lines . ) 2. In any parallelogram either of the parallelograms ...
Page 35
... rectangle under the two lines is equal to the sum of the rectangles under the undivided line ( A ) and the several ... rectangle BL is equal to the rectangles BG , DK and EL ; but the rectangle BL is the rectangle under A and BC , for BF ...
... rectangle under the two lines is equal to the sum of the rectangles under the undivided line ( A ) and the several ... rectangle BL is equal to the rectangles BG , DK and EL ; but the rectangle BL is the rectangle under A and BC , for BF ...
Page 36
... rectangle under X and AB , or the square of AB ( 1 ) hypoth . ( 1 ) , is equal to the sum of the rectangles under X ... rectangle under the whole line ( AB ) and either part ( AC ) is equal to the square of that part ( AC ) together with ...
... rectangle under X and AB , or the square of AB ( 1 ) hypoth . ( 1 ) , is equal to the sum of the rectangles under X ... rectangle under the whole line ( AB ) and either part ( AC ) is equal to the square of that part ( AC ) together with ...
Page 37
... rectangle AG and GD . B 1 . But OF is the square of OB ( 1 ) , and EK is the ( 2 ) constr & square of AO , for EG is equal to AO ( 2 ) ; and AG prop.34.B.1 ( 3 ) Def.31 . and GD together are equal to double the rectangle B. 1 . under ...
... rectangle AG and GD . B 1 . But OF is the square of OB ( 1 ) , and EK is the ( 2 ) constr & square of AO , for EG is equal to AO ( 2 ) ; and AG prop.34.B.1 ( 3 ) Def.31 . and GD together are equal to double the rectangle B. 1 . under ...
Page 38
... rectangle under the un- equal parts ( AD and DB ) , together with the square of the intermediate part ( CD ) is ... rectangle AG is equal to the gnomon CHL ( 4 ) , add ( 4 ) Ar . 2. to both the square FL , and the rectangle AG together ...
... rectangle under the un- equal parts ( AD and DB ) , together with the square of the intermediate part ( CD ) is ... rectangle AG is equal to the gnomon CHL ( 4 ) , add ( 4 ) Ar . 2. to both the square FL , and the rectangle AG together ...
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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.