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 67
... rectangle AE is equal to the rectangles AD , CE . 2. AE is the rectangle contained by AB , BC , for it is contained ... twice the rectangle contained by the parts . Let the straight line AB be divided into any two parts in C. Then ...
... rectangle AE is equal to the rectangles AD , CE . 2. AE is the rectangle contained by AB , BC , for it is contained ... twice the rectangle contained by the parts . Let the straight line AB be divided into any two parts in C. Then ...
Side 69
... rectangle AC , CB ; wherefore 14. AG , GE are equal to twice the rectangle AC , CB ; and HF , CK are the squares on AC , CB ; wherefore 15. The four figures HF , CK , AG , GE , are equal to the squares on AC , CB , and twice the rectangle ...
... rectangle AC , CB ; wherefore 14. AG , GE are equal to twice the rectangle AC , CB ; and HF , CK are the squares on AC , CB ; wherefore 15. The four figures HF , CK , AG , GE , are equal to the squares on AC , CB , and twice the rectangle ...
Side 72
... twice the rectangle con- tained by the whole and that part , together with the square on the other part . Let the straight line AB be divided into any two parts in the point C. Then the squares on AB , BC shall be equal to twice the ...
... twice the rectangle con- tained by the whole and that part , together with the square on the other part . Let the straight line AB be divided into any two parts in the point C. Then the squares on AB , BC shall be equal to twice the ...
Side 73
... twice the rectangle AB , BC , and the square on AC ; but the gnomon AKF , together with the squares CK , HF , make up the whole figure ADEB and CK , which are the squares on AB and BC ; therefore 7. The squares on AB and BC are equal to ...
... twice the rectangle AB , BC , and the square on AC ; but the gnomon AKF , together with the squares CK , HF , make up the whole figure ADEB and CK , which are the squares on AB and BC ; therefore 7. The squares on AB and BC are equal to ...
Side 81
... rectangle AB , BH is equal to the square on AH . Q.E.F. PROPOSITION 12. - Theorem . In obtuse - angled triangles ... twice the rectangle contained by the side upon which , when produced , the perpendicular falls , and the straight ...
... rectangle AB , BH is equal to the square on AH . Q.E.F. PROPOSITION 12. - Theorem . In obtuse - angled triangles ... twice the rectangle contained by the side upon which , when produced , the perpendicular falls , and the straight ...
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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.