The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthDesilver, Thomas & Company, 1838 - 416 sider |
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Resultat 1-5 av 85
Side 11
... sides of the one equal to two sides of the other , each to each ; and have likewise the angles con- tained by those ... B A CE D F For if the triangle ABC be applied to DEF , so that the point A may be on D , and the straight line AB ...
... sides of the one equal to two sides of the other , each to each ; and have likewise the angles con- tained by those ... B A CE D F For if the triangle ABC be applied to DEF , so that the point A may be on D , and the straight line AB ...
Side 15
... sides BA , CA do not coincide with the sides ED , FD but have a different situation , as EG , FG ; then upon the same base EF , and upon the same side of it , there can be two triangles that have their sides which are terminated in one ...
... sides BA , CA do not coincide with the sides ED , FD but have a different situation , as EG , FG ; then upon the same base EF , and upon the same side of it , there can be two triangles that have their sides which are terminated in one ...
Side 21
... side . * Let ABC be a triangle ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to the point D ...
... side . * Let ABC be a triangle ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to the point D ...
Side 22
... sides BA , AC are greater than BE , EC : again , because the two sides CE , ED of the triangle CED are greater than CD , add DB to each of these ; therefore the sides CE , EB are greater than CD , DB ; but it has been shown that BA , AC ...
... sides BA , AC are greater than BE , EC : again , because the two sides CE , ED of the triangle CED are greater than CD , add DB to each of these ; therefore the sides CE , EB are greater than CD , DB ; but it has been shown that BA , AC ...
Side 23
... sides of which shall be equal to the three straight lines D CD , DE , CE ... side which is not greater than the other , and at the point D , in the straight ... BA , AC are equal to the two ED , DG , each to each , and the angle * See ...
... sides of which shall be equal to the three straight lines D CD , DE , CE ... side which is not greater than the other , and at the point D , in the straight ... BA , AC are equal to the two ED , DG , each to each , and the angle * See ...
Vanlige uttrykk og setninger
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference Co-S cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC square of BC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 41 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.
Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 256 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 129 - 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 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Side 20 - ANY two angles of a triangle are together less than two right angles.