The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With the Elements of Plane Trigonometry, and an Appendix in Four Books : With Notes and IllustrationsLongmans, Green, 1845 - 352 sider |
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Side iii
... Prove Euc . I. 17 , without producing any side . 10. Prove the first and second parts of Euc . I. 28 , independ- ently of I. 27 , and of one another : and from each , when proved , de- rive I. 27 , and the remaining part of I. 28 . 11 ...
... Prove Euc . I. 17 , without producing any side . 10. Prove the first and second parts of Euc . I. 28 , independ- ently of I. 27 , and of one another : and from each , when proved , de- rive I. 27 , and the remaining part of I. 28 . 11 ...
Side ix
... prove that mA + B : B :: mC + D : D. 2. On the same hypothesis , prove that mA + nB : pA + qB :: mC + nD : pC + qD . 3. On the same hypothesis , still , prove that A2 + B2 : A2 - B2 :: C2 + D : C2 - D2 . 4. Prove also that A2 + AB + B2 ...
... prove that mA + B : B :: mC + D : D. 2. On the same hypothesis , prove that mA + nB : pA + qB :: mC + nD : pC + qD . 3. On the same hypothesis , still , prove that A2 + B2 : A2 - B2 :: C2 + D : C2 - D2 . 4. Prove also that A2 + AB + B2 ...
Side 4
... proved . Thus , as will appear hereafter , it can be proved , that if a quadrilateral have all its sides equal , and have one right angle , it will have all its angles right angles : and till the 32d proposition and its corollaries are ...
... proved . Thus , as will appear hereafter , it can be proved , that if a quadrilateral have all its sides equal , and have one right angle , it will have all its angles right angles : and till the 32d proposition and its corollaries are ...
Side 6
... proved that proposition . He will find it useful also , in other instances , to postpone the serious consideration of definitions , postulates , and axioms , till they come to be employed in the propositions ; but he should then make ...
... proved that proposition . He will find it useful also , in other instances , to postpone the serious consideration of definitions , postulates , and axioms , till they come to be employed in the propositions ; but he should then make ...
Side 7
... proved that CA is equal to AB ; therefore , CA , CB are each of them equal to AB : but things which are equal to the same are equal ( I. axiom 1 ) to one another ; therefore CA is equal to CB ; wherefore CA , AB , BC are equal to one ...
... proved that CA is equal to AB ; therefore , CA , CB are each of them equal to AB : but things which are equal to the same are equal ( I. axiom 1 ) to one another ; therefore CA is equal to CB ; wherefore CA , AB , BC are equal to one ...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... James Thomson, gen,James Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained corollary cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB.-To produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol scholium segments semicircle sides similar solid angles square of AC straight line drawn tangent THEOR.-If third triangle ABC trigonometry triplicate ratio vertex vertical angle wherefore
Populære avsnitt
Side 130 - 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 45 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Side 2 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Side 50 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Side 38 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Side 7 - If two triangles have two sides of the one equal to two sides of the...
Side 27 - 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 27 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Side 15 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Side 36 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.