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 24
... relation will the angles which are opposite to each other at the vertex M , bear to each other ? A. They will be equal to each other . Q. How can you prove it ? B D M α A A. Because , if you add the same angle a , first to b , and then ...
... relation will the angles which are opposite to each other at the vertex M , bear to each other ? A. They will be equal to each other . Q. How can you prove it ? B D M α A A. Because , if you add the same angle a , first to b , and then ...
Σελίδα 25
... relation must these triangles bear to each other ? A. They must be equal . Q. Supposing in this diagram the side a b equal to AB ; the angle at a equal to the angle at A , and the angle at b equal to the angle at B ; how can you prove ...
... relation must these triangles bear to each other ? A. They must be equal . Q. Supposing in this diagram the side a b equal to AB ; the angle at a equal to the angle at A , and the angle at b equal to the angle at B ; how can you prove ...
Σελίδα 26
... relation do you here discover be- tween the equal sides and angles ? A. That the equal angles c , C , are opposite to the equal sides a b , AB respectively . QUERY VII . If two straight lines are both perpendicular to another straight ...
... relation do you here discover be- tween the equal sides and angles ? A. That the equal angles c , C , are opposite to the equal sides a b , AB respectively . QUERY VII . If two straight lines are both perpendicular to another straight ...
Σελίδα 29
... relation exists be- B D tween these two lines ? A. They are parallel to each other . Q. How can you prove it by this diagram ? The line IF is bisected in O , and , from that point O , a perpendicular OP is dropped to the line AB , and ...
... relation exists be- B D tween these two lines ? A. They are parallel to each other . Q. How can you prove it by this diagram ? The line IF is bisected in O , and , from that point O , a perpendicular OP is dropped to the line AB , and ...
Σελίδα 30
... relation would the lines AB , CD , then bear to each other ? A. They would still be parallel . Q. How do you prove this ? A. For if the angle AEF is equal to the angle EFD , the angles AEF and CFN will also be equal ; because EFD and ...
... relation would the lines AB , CD , then bear to each other ? A. They would still be parallel . Q. How do you prove this ? A. For if the angle AEF is equal to the angle EFD , the angles AEF and CFN will also be equal ; because EFD and ...
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...