Elements of Plane Geometry: For the Use of SchoolsLewis & Sampson, 1844 - 96 σελίδες |
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Αποτελέσματα 1 - 5 από τα 21.
Σελίδα 9
... the one half , one third , & c . of the same or equal things , are equal to each other . 4. If equals be added to , or taken from equals , the results will be equal . 5. If equals be added to , or taken from BOOK I. ] AXIOMS .
... the one half , one third , & c . of the same or equal things , are equal to each other . 4. If equals be added to , or taken from equals , the results will be equal . 5. If equals be added to , or taken from BOOK I. ] AXIOMS .
Σελίδα 12
... third be drawn so as to make with them ad- jacent angles , which , taken together , are equal to two right angles , the two first lines will form but one con- tinued straight line . Let the two straight lines , AB , CB , meet in the ...
... third be drawn so as to make with them ad- jacent angles , which , taken together , are equal to two right angles , the two first lines will form but one con- tinued straight line . Let the two straight lines , AB , CB , meet in the ...
Σελίδα 17
... third straight line , the alternate angles will be equal . Let the parallels AB , CD , be cut by A the line EF ; then we Fig . 9 . E have to prove that the C alternate angles AIF , EOD , are equal . The angles EIB , EOD , are equal by ...
... third straight line , the alternate angles will be equal . Let the parallels AB , CD , be cut by A the line EF ; then we Fig . 9 . E have to prove that the C alternate angles AIF , EOD , are equal . The angles EIB , EOD , are equal by ...
Σελίδα 18
... third , making the al- ternate angles equal , the two first lines are parallel . Let the angles AIF , EOD , be equal ; then we have to prove that AB , CD , are parallel . If they are not parallel , draw through I , the line HK , par ...
... third , making the al- ternate angles equal , the two first lines are parallel . Let the angles AIF , EOD , be equal ; then we have to prove that AB , CD , are parallel . If they are not parallel , draw through I , the line HK , par ...
Σελίδα 19
... third , they will be parallel to each other . Let CD , EF , be paral- lel to AB ; then we have to prove that they will be par- allel to each other . A C E Fig . 13 . I H B -D Draw IH perpendicular to AB , it will also ( by Prop . 9 ...
... third , they will be parallel to each other . Let CD , EF , be paral- lel to AB ; then we have to prove that they will be par- allel to each other . A C E Fig . 13 . I H B -D Draw IH perpendicular to AB , it will also ( by Prop . 9 ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Plane Geometry: For the Use of Schools - Primary Source Edition Nicholas Tillinghast Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles allel alternate angles altitude angle ABC angles ABD angles is equal antecedent and consequent B. I. Ax base centre circle whose radius circumference circumscribed circumscribed circle Converse of Prop describe an arc diagonal diameter divide draw the line equal angles equal B. I. Prop equal chords equal Prop equal respectively equiangular equivalent feet given angle given line given point given side half hence the triangles hypotenuse included angle inscribed angle Let the triangles line drawn linear units longer than AC multiplied number of sides oblique lines parallel to CD parallelogram perimeter perpendicular PROBLEM prove radii rectangle regular polygons respectively equal right angles Prop right-angled triangle Scholium sides AC similar subtended tangent THEOREM three sides triangles ABC triangles are equal vertex
Δημοφιλή αποσπάσματα
Σελίδα 31 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Σελίδα 63 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Σελίδα 70 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 53 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 87 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Σελίδα 54 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Σελίδα 81 - 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.
Σελίδα 59 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Σελίδα 61 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.
Σελίδα 82 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.