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 51
Side 93
... fourth , when any equimultiples whatsoever of the first and third being taken , and any equimulti- ples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is ...
... fourth , when any equimultiples whatsoever of the first and third being taken , and any equimulti- ples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is ...
Side 94
... fourth ; and , on the contrary , the third is said to have to the fourth a less ratio than the first has to the second . VIII . Analogy , or proportion , is the similitude of ratios . ' IX . Proportion consists in three terms at least ...
... fourth ; and , on the contrary , the third is said to have to the fourth a less ratio than the first has to the second . VIII . Analogy , or proportion , is the similitude of ratios . ' IX . Proportion consists in three terms at least ...
Side 95
... fourth ; or that the first is to the third , as the second to the fourth ; as is shown in the 16th prop . of this 5th book . * XIV . Invertendo , by inversion ; when there are four proportionals , and it is inferred , that the second is ...
... fourth ; or that the first is to the third , as the second to the fourth ; as is shown in the 16th prop . of this 5th book . * XIV . Invertendo , by inversion ; when there are four proportionals , and it is inferred , that the second is ...
Side 96
... fourth of the first rank , so is the third from the last to the last but two of the second rank and so on in a cross order : and the inference is as in the 18th definition . It is demonstrated in the 23d Prop . of book 5 . AXIOMS . I ...
... fourth of the first rank , so is the third from the last to the last but two of the second rank and so on in a cross order : and the inference is as in the 18th definition . It is demonstrated in the 23d Prop . of book 5 . AXIOMS . I ...
Side 97
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . A D Let ...
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . A D Let ...
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.