The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin1874 |
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Side 161
... greater contains the less a certain number of times exactly . " 3 . " Ratio is a mutual relation of two magnitudes of the same kind to one another , in respect of quantity . " 4 . Magnitudes are said to have a ratio to one another ...
... greater contains the less a certain number of times exactly . " 3 . " Ratio is a mutual relation of two magnitudes of the same kind to one another , in respect of quantity . " 4 . Magnitudes are said to have a ratio to one another ...
Side 174
... ratio to the same magnitude ; and the same has the same ratio to equal magnitudes . Let A and B be equal magnitudes ... greater than F , E is greater than F ; and if equal , equal ; and if less , less ; but D , E are any ...
... ratio to the same magnitude ; and the same has the same ratio to equal magnitudes . Let A and B be equal magnitudes ... greater than F , E is greater than F ; and if equal , equal ; and if less , less ; but D , E are any ...
Side 175
... greater has a greater ratio to any other magnitude than the less has ; and the same magnitude has a greater ratio to the less of two other magnitudes , than it has to the greater . Let AB , BC be two unequal magnitudes , of which AB is the ...
... greater has a greater ratio to any other magnitude than the less has ; and the same magnitude has a greater ratio to the less of two other magnitudes , than it has to the greater . Let AB , BC be two unequal magnitudes , of which AB is the ...
Side 177
... greater than the other ; let A be the greater ; then , by what was shown in the preceding proposition , there are some equimultiples of A and B , and some multiple of C , such , that ... greater ratio than B BOOK V.- PROP . IX . 177.
... greater than the other ; let A be the greater ; then , by what was shown in the preceding proposition , there are some equimultiples of A and B , and some multiple of C , such , that ... greater ratio than B BOOK V.- PROP . IX . 177.
Side 180
... ratio which the third has to the fourth , but the third to the fourth , a greater ratio than the fifth has to the sixth ; the first shall also have to the ... greater than L ; and whatever multiple G is of 180 EUCLID'S ELEMENTS .
... ratio which the third has to the fourth , but the third to the fourth , a greater ratio than the fifth has to the sixth ; the first shall also have to the ... greater than L ; and whatever multiple G is of 180 EUCLID'S ELEMENTS .
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The Elements of Euclid, Containing the First Six Books, with a Selection of ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
AB is equal AC is equal adjacent angles angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF angle equal base BC bisected centre circle ABC circumference constr Demonstration diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle given circle given point given straight line gnomon greater ratio inscribed less Let ABC Let the straight meet multiple opposite angle parallel to BC parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION rectangle contained remaining angle right angles segment similar square on AC straight line AB straight line BC straight line drawn Theorem three straight lines tiple touches the circle triangle ABC triangle DEF twice the rectangle wherefore
Populære avsnitt
Side 1 - 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.
Side 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Side 232 - If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let...
Side 112 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 209 - ... triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Side 269 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Side 199 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Side 63 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts...
Side 32 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.