The First Six Books with NotesR. Milliken, 1822 - 179 σελίδες |
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Αποτελέσματα 1 - 5 από τα 13.
Σελίδα 8
... CD . Because the sides AC and AD of the triangle CAD are equal ( 6 ) , the ... given line . PROP . VIII . THEOR . If two triangles , ( ABC and EFD ) have two ... contained by the equal sides are equal . For if the equal bases AC and ED be ...
... CD . Because the sides AC and AD of the triangle CAD are equal ( 6 ) , the ... given line . PROP . VIII . THEOR . If two triangles , ( ABC and EFD ) have two ... contained by the equal sides are equal . For if the equal bases AC and ED be ...
Σελίδα 14
... CD ; therefore the two sides BA and AC taken together are greater than BD , DC or the third side BC . Thus bisecting ... contain a greater angle . Produce BD to E. The sides BA and AE of the tri- angle ABE are greater than the third side ...
... CD ; therefore the two sides BA and AC taken together are greater than BD , DC or the third side BC . Thus bisecting ... contain a greater angle . Produce BD to E. The sides BA and AE of the tri- angle ABE are greater than the third side ...
Σελίδα 32
... contain that angle , shall be equal to the diffe- rence between the squares ... CD and DB ( 2 ) , or taking away the common square of DB , equal to the ... contain the right angle , and ( 2 ) Prop . 3. equal to the other BC ( 2 ) , and ...
... contain that angle , shall be equal to the diffe- rence between the squares ... CD and DB ( 2 ) , or taking away the common square of DB , equal to the ... contain the right angle , and ( 2 ) Prop . 3. equal to the other BC ( 2 ) , and ...
Σελίδα 89
... given circle ( CAD ) to inscribe an equilateral and Fig . 18 . equiangular quindecagon . Let CD be the side of an ... CD , since it is the third part of the whole circum- ference , contains five of these parts , in like manner the ...
... given circle ( CAD ) to inscribe an equilateral and Fig . 18 . equiangular quindecagon . Let CD be the side of an ... CD , since it is the third part of the whole circum- ference , contains five of these parts , in like manner the ...
Σελίδα 94
... contained in any third , so other contained in the same third . often is the first equal Cor . 3. If there be four ... CD and EF ) of which the first is greater than the second , and the third is equal to the fourth , the first is not ...
... contained in any third , so other contained in the same third . often is the first equal Cor . 3. If there be four ... CD and EF ) of which the first is greater than the second , and the third is equal to the fourth , the first is not ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 25 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 3 - A rhombus is that which has all its sides equal, but its angles are not right angles.