The First Six Books with NotesR. Milliken, 1822 - 179 sider |
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Side 35
... divided into any number of parts ( BD , DE , EC ' ) , Fig . 1 . the rectangle under the two lines is equal to the sum of the rectangles under the undivided line ( A ) and the several parts of the divided line ( BD , DE , EC ) . From the ...
... divided into any number of parts ( BD , DE , EC ' ) , Fig . 1 . the rectangle under the two lines is equal to the sum of the rectangles under the undivided line ( A ) and the several parts of the divided line ( BD , DE , EC ) . From the ...
Side 36
... divided into any two parts ( in C ) , the rectangle under the whole line ( AB ) and either part ( AC ) is equal to the square of that part ( AC ) together with the rectangle under the parts ( AC and CB . ) On AC describe the square ADFC ...
... divided into any two parts ( in C ) , the rectangle under the whole line ( AB ) and either part ( AC ) is equal to the square of that part ( AC ) together with the rectangle under the parts ( AC and CB . ) On AC describe the square ADFC ...
Side 37
... divided into any two parts Fig . 6 . ( in O ) , the square of the whole line is equal to the sum of the squares of the parts and twice the rectangle under the parts . On AC describe the square ACDB , draw CB , and through O draw OK ...
... divided into any two parts Fig . 6 . ( in O ) , the square of the whole line is equal to the sum of the squares of the parts and twice the rectangle under the parts . On AC describe the square ACDB , draw CB , and through O draw OK ...
Side 39
... divided in E and F. Let the lines be bisected in G and H , and as the lines are equal ( 1 ) , their halves are equal , and therefore the squares of the halves ( 2 ) , but the rectangles under AE ( 2 ) Cor . 1 . and EB , and under CF and ...
... divided in E and F. Let the lines be bisected in G and H , and as the lines are equal ( 1 ) , their halves are equal , and therefore the squares of the halves ( 2 ) , but the rectangles under AE ( 2 ) Cor . 1 . and EB , and under CF and ...
Side 42
... divided into any two parts , the squares of the whole line ( AB ) and either segment ( CB ) are together equal to double the rectangle under the whole and that segment , together with the square of the other segment . Describe the ...
... divided into any two parts , the squares of the whole line ( AB ) and either segment ( CB ) are together equal to double the rectangle under the whole and that segment , together with the square of the other segment . Describe the ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 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.
Side 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 3 - A rhombus is that which has all its sides equal, but its angles are not right angles.