Euclid's Elements of plane geometry [book 1-6] with explanatory appendix, and supplementary propositions, by W.D. Cooley1840 |
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Σελίδα 5
... means a great abridgment has been effected , without omitting a single step in the reasoning , or in the slightest degree impairing its strength and validity . The Six Books of the Elements , here comprised in only 120 mo- derately ...
... means a great abridgment has been effected , without omitting a single step in the reasoning , or in the slightest degree impairing its strength and validity . The Six Books of the Elements , here comprised in only 120 mo- derately ...
Σελίδα 8
... means of the dead languages . The study of Greek and Latin at an early age , considered as a mental exercise , induces the dangerous habit of learning by rote ; and with respect to its immediate and appropriate result , it only teaches ...
... means of the dead languages . The study of Greek and Latin at an early age , considered as a mental exercise , induces the dangerous habit of learning by rote ; and with respect to its immediate and appropriate result , it only teaches ...
Σελίδα 10
... mean , the sense of complete certainty -the thorough conviction which attends mathematical deductions . On all other subjects men deal with opinions more or less true - with principles and conclusions alike liable to be controverted ...
... mean , the sense of complete certainty -the thorough conviction which attends mathematical deductions . On all other subjects men deal with opinions more or less true - with principles and conclusions alike liable to be controverted ...
Σελίδα 12
... means , the young student will perceive the general nature of the abstract reasonings in which he is engaged , and will become familiar with the fact , that the diagram in general represents but one out of innumerable cases . It must ...
... means , the young student will perceive the general nature of the abstract reasonings in which he is engaged , and will become familiar with the fact , that the diagram in general represents but one out of innumerable cases . It must ...
Σελίδα 16
... means A with B added to it , or the sum of A and B. means the difference of A and B , or A with B taken from it . The sign of multiplication is X ; thus AX B signifies A multiplied by B. In speaking of rectangles , the adjacent sides ...
... means A with B added to it , or the sum of A and B. means the difference of A and B , or A with B taken from it . The sign of multiplication is X ; thus AX B signifies A multiplied by B. In speaking of rectangles , the adjacent sides ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ACDB adjacent angles angles equal antecedent Axioms base bisected centre chord circumference coincide consequently Const definition demonstrated describe diagonal diameter difference divided draw equal angles equal Prop equal sides equiangular equilateral triangle equimultiples Euclid Euclid's Elements external angle extremities fore fourth fractional Geometry given angle given circle given line given point given straight line given triangle greater hypotenuse inscribed internal intersect isosceles triangle less line drawn lines be drawn magnitudes manner meeting multiple opposite angles parallel parallelogram perpendicular point of contact PROB produced proportional Proposition quadrilateral figure rectangle contained rectilinear figure remaining angles respectively equal right angle segment semiperimeter sides AC sides equal square of half subtending taken tangent THEOR third triangles ABC unequal vertex whole line
Δημοφιλή αποσπάσματα
Σελίδα 126 - 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'.
Σελίδα 155 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 83 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Σελίδα 129 - ... figures are to one another in the duplicate ratio of their homologous sides.
Σελίδα 47 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 90 - BFE : (i. def. 10.) therefore, in the two triangles, EAF, EBF, there are two angles in the one equal to two angles in the other, each to each ; and the side EF, which is opposite to one of the equal angles in each, is common to both ; therefore the other sides are equal ; (i.
Σελίδα 117 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.
Σελίδα 56 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Σελίδα 60 - Iff 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.
Σελίδα 78 - Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible. let the two similar segments of circles, viz. ACB' ADB be upon the same side of the same straight line AB, not coinciding with one another.