The Elements of geometry [Euclid book 1-3] in general terms, with notes &c. &c. Also a variety of problems & theorems. [Ed. by J. Luby. With] The elements of plane geometry, comprising the definitions of the fifth book, and the sixth book in general terms, with notes [&c.] by J. Luby [described as] Pt. 31833 |
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Αποτελέσματα 1 - 5 από τα 21.
Σελίδα 4
... antecedent , and the second the consequent . It is to be observed , that ratio of equality , and equality of ratio are not to be confounded ; for they are by no means synonymous terms , since two or more ratios may be , though the ...
... antecedent , and the second the consequent . It is to be observed , that ratio of equality , and equality of ratio are not to be confounded ; for they are by no means synonymous terms , since two or more ratios may be , though the ...
Σελίδα 5
... antecedent 16 are contained in its conse- quent 27 as often as the equi - submultiples 1 , 2 , 4 , of the antecedent 8 are contained in its consequent 13 ; yet if we take the equi - submultiples 1 and of the antecedents 16 and 8 , we ...
... antecedent 16 are contained in its conse- quent 27 as often as the equi - submultiples 1 , 2 , 4 , of the antecedent 8 are contained in its consequent 13 ; yet if we take the equi - submultiples 1 and of the antecedents 16 and 8 , we ...
Σελίδα 6
... antecedent . When this is the case , the middle term is a mean proportional between the extremes . 10. When three magnitudes are proportional ( A : B :: B : C ) then the first is said to have to the third ( A : C ) a duplicate ratio of ...
... antecedent . When this is the case , the middle term is a mean proportional between the extremes . 10. When three magnitudes are proportional ( A : B :: B : C ) then the first is said to have to the third ( A : C ) a duplicate ratio of ...
Σελίδα 7
... antecedents are said to be homo- logous to the antecedents , and the consequents to the con- sequents . Thus if A : B :: C : D , then A is homologous to C , and B to D. Geometers make use of the following terms , to express certain ...
... antecedents are said to be homo- logous to the antecedents , and the consequents to the con- sequents . Thus if A : B :: C : D , then A is homologous to C , and B to D. Geometers make use of the following terms , to express certain ...
Σελίδα 8
... antecedent is made consequent , and the consequent , antecedent . If A : B :: C : D , then in- vertendo , B : A :: D : C ; this is called inverse ratio . The def . is proved by Prop . 20 , Book 5 . 16. Componendo ; when it is concluded ...
... antecedent is made consequent , and the consequent , antecedent . If A : B :: C : D , then in- vertendo , B : A :: D : C ; this is called inverse ratio . The def . is proved by Prop . 20 , Book 5 . 16. Componendo ; when it is concluded ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent altitude ANALYSIS angle contained antecedent assumed bisecting line chord circumference circumscribing circle connecting line construct conterminous dedu diagonal diameter directum divided draw a right drawn line equal angles equiangular equilateral triangle evident external angle extremity given angle given circle given figure given in position given line given point given ratio given right line given triangle half the difference half the given hypotenuse inscribed intercept intersect isosceles triangle less lesser let fall line bisecting lines be drawn magnitude mean proportional meet opposite angle opposite side parallelogram pass perpendicular point of bisection point of contact polygons PROB PROP radii radius rect rectangle required triangle respectively right angled triangle secant segts semicircle side subtending similar square Suppose tangent THEOR triangle ABC vertex vertical angle whole line
Δημοφιλή αποσπάσματα
Σελίδα 100 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 11 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Σελίδα 130 - The angle at the centre of a circle is double the angle at the circumference on the same arc.
Σελίδα 135 - ... a circle. The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary ; and the converse.
Σελίδα 32 - ... polygons are to each other in the duplicate ratio of their homologous sides.
Σελίδα 37 - In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the sum of the squares described on the sides which contain the right angle.
Σελίδα 124 - If from a point within a circle more than two equal straight lines can be drawn to the circumference, that point is the centre of the circle.
Σελίδα 6 - Convertendo ; when it is concluded, that, if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.
Σελίδα 10 - If two triangles have two sides of the one equal to two sides of the other, each to each, and" have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides equal to them, of the other. Let ABC, DEF be two triangles, having the two sides AB, AC, equal to the two sides DE, DF, each to each, viz.
Σελίδα 118 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.