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 12
... AC . D Λ For , if AB be not equal to AC , † one of them is greater than the other let AB be the greater , and from it cut off ( I. 3 ) BD equal to AC , the less , and join DC . Then , because in the triangles DBC , ACB , DB is equal to AC ...
... AC . D Λ For , if AB be not equal to AC , † one of them is greater than the other let AB be the greater , and from it cut off ( I. 3 ) BD equal to AC , the less , and join DC . Then , because in the triangles DBC , ACB , DB is equal to AC ...
Side 13
... AC is equal to AD , and likewise BC to BD , is false . A C D B E P But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ...
... AC is equal to AD , and likewise BC to BD , is false . A C D B E P But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ...
Side 21
... AC ; and join DC . Because DA is equal to AC , the angle ADC is likewise equal ( I. 5 ) to ACD ; but the angle BCD is greater ( I. ax . 9 ) than ACD : therefore the ... square inches Find the side of a square field, containing three acres.
... AC ; and join DC . Because DA is equal to AC , the angle ADC is likewise equal ( I. 5 ) to ACD ; but the angle BCD is greater ( I. ax . 9 ) than ACD : therefore the ... square inches Find the side of a square field, containing three acres.
Side 38
... square upon a given straight line . Let AB be a given straight line ; it is required to describe a square upon it . C D From the point A draw ( I. 11 ) AC at right angles to AB , and make AD equal to AB : through the point D draw ( 1.31 ) ...
... square upon a given straight line . Let AB be a given straight line ; it is required to describe a square upon it . C D From the point A draw ( I. 11 ) AC at right angles to AB , and make AD equal to AB : through the point D draw ( 1.31 ) ...
Side 40
... square which is described upon the hypotenuse , that is , the side subtending the right angle , is equal to the squares described upon the sides which contain the right angle ... AC : wherefore the square upon BC is 40 [ ROOK I. THE ELEMENTS.
... square which is described upon the hypotenuse , that is , the side subtending the right angle , is equal to the squares described upon the sides which contain the right angle ... AC : wherefore the square upon BC is 40 [ ROOK I. THE ELEMENTS.
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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 - 2016 |
Almindelige termer og sætninger
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
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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.