First lessons in Plane Geometry. Together with an application of them to the solution of problems, etcCarter and Hendee, 1830 - 12 σελίδες |
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Σελίδα 18
... one another . TRUTH III . If equals be added to equals , the wholes are equal . TRUTH IV . If equals be taken from equals , the re- mainders are equal . TRUTH V. The whole is greater than any one of 18 GEOMETRY . Axioms.
... one another . TRUTH III . If equals be added to equals , the wholes are equal . TRUTH IV . If equals be taken from equals , the re- mainders are equal . TRUTH V. The whole is greater than any one of 18 GEOMETRY . Axioms.
Σελίδα 19
Francis Joseph Grund. TRUTH V. The whole is greater than any one of its parts . TRUTH VI . The sum of all the parts is equal to the whole . TRUTH VII . Magnitudes , which coincide with one another , that is , which exactly fill the same ...
Francis Joseph Grund. TRUTH V. The whole is greater than any one of its parts . TRUTH VI . The sum of all the parts is equal to the whole . TRUTH VII . Magnitudes , which coincide with one another , that is , which exactly fill the same ...
Σελίδα 22
... whole of your reasoning , and prove that two straight lines can- not have any part common , without coinciding with each other throughout , and making but one and the same straight line ? * * QUERY III . * If a straight line meets ...
... whole of your reasoning , and prove that two straight lines can- not have any part common , without coinciding with each other throughout , and making but one and the same straight line ? * * QUERY III . * If a straight line meets ...
Σελίδα 28
... whole demonstra- tion , and show that if one of two parallel lines is perpendicular to a straight line , the other line must also be perpendicular to it ? * * If a straight line MN , cuts two other straight 28 GEOMETRY .
... whole demonstra- tion , and show that if one of two parallel lines is perpendicular to a straight line , the other line must also be perpendicular to it ? * * If a straight line MN , cuts two other straight 28 GEOMETRY .
Σελίδα 35
... ; and be- cause EF is also parallel to AB , every point in the line EF must also be at an equal distance from the line AB ; and therefore ( in Fig . I. ) the whole distance between the lines CD and EF , or ( in Fig . II . ) GEOMETRY . 35.
... ; and be- cause EF is also parallel to AB , every point in the line EF must also be at an equal distance from the line AB ; and therefore ( in Fig . I. ) the whole distance between the lines CD and EF , or ( in Fig . II . ) GEOMETRY . 35.
Άλλες εκδόσεις - Προβολή όλων
First Lessons in Plane Geometry: Together with an Application of Them to the ... Francis Joseph Grund Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2009 |
First Lessons in Plane Geometry: Together with an Application of Them to the ... Francis Joseph Grund Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2009 |
Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent angles angle ABC angle ACB angle opposite angle x basis and height bisected called centre chord circum circumference circumscribed circle consequently construct the triangle DEMON diagonal diameter draw the lines equal angles exterior angle figure ABCDEF found by multiplying fourth term geometrical figures geometrical proportion given angle given circle given straight line given triangle hypothenuse isosceles triangle line AB line AC line CD line MN LUDOLPH VAN CEULEN mean proportional number of sides parallel lines parallelogram perpendicular points of division PROBLEM prove quadrilateral Query 11 radii radius ratio rectilinear figure regular polygon ABCDEF remaining sides Remark right angles right-angular triangle Sect semicircle side AB side AC similar triangles smaller SOLUTION square feet square inches square seconds tangent third line three angles three sides trapezoid trian triangle ABC triangle are equal vertex zoid
Δημοφιλή αποσπάσματα
Σελίδα 195 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Σελίδα 94 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the...
Σελίδα 211 - HDG, the corresponding sides are proportional (page 70, 4thly) ; therefore we have the proportion ED : DG =AD : HD (II.) This last proportion has the first ratio common with the first proportion ; consequently the two remaining ratios are in a geometrical proportion (Theory of Prop., Prin. 3d) ; that is, we have AD : HD = DG: BD; and as, in...
Σελίδα 173 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Σελίδα 176 - 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 175 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Σελίδα 129 - Now, since the areas of similar polygons are to each other as the squares of their homologous sides...