Elements of Geometry, After Legendre, with a Selection of Geometrical Exercises, and Hints for the Solution of the Same |
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Αποτελέσματα 1 - 5 από τα 55.
Σελίδα 26
... manner that the angle ACE is equal to its opposite angle BCD . D SCHOLIUM . - The four angles formed about a point by two straight lines which cut each other , are , together , equal to four right angles ; for the angles ACE , BCE ...
... manner that the angle ACE is equal to its opposite angle BCD . D SCHOLIUM . - The four angles formed about a point by two straight lines which cut each other , are , together , equal to four right angles ; for the angles ACE , BCE ...
Σελίδα 27
... manner , since the angle F is equal to the angle C , the line FD will fall along CA , and the point D will be found somewhere in the side CA. Hence , the point D , which is found at the same time in the two lines BA and CA , must fall ...
... manner , since the angle F is equal to the angle C , the line FD will fall along CA , and the point D will be found somewhere in the side CA. Hence , the point D , which is found at the same time in the two lines BA and CA , must fall ...
Σελίδα 28
... manner BD < BA + AD ; add DC to each and we have But we have just found BD + DC < BA + AC . BO + OC < BD + DC . Therefore , still more is BO + OC < BA + AC . SCHOLIUM . When two triangles , ABC and EBC , which have a com- mon side , BC ...
... manner BD < BA + AD ; add DC to each and we have But we have just found BD + DC < BA + AC . BO + OC < BD + DC . Therefore , still more is BO + OC < BA + AC . SCHOLIUM . When two triangles , ABC and EBC , which have a com- mon side , BC ...
Σελίδα 30
... manner it may be shown that the angle BE , and that the angle C = F. SCHOLIUM.It may be observed that the equal angles are opposite to the equal sides : thus , the equal angles A and D are opposite to the equal sides BC , EF ...
... manner it may be shown that the angle BE , and that the angle C = F. SCHOLIUM.It may be observed that the equal angles are opposite to the equal sides : thus , the equal angles A and D are opposite to the equal sides BC , EF ...
Σελίδα 33
... be greater or less than AE ; but both of these results are contrary to the hypothesis ; therefore , BC = BE . COR . 4. In like manner , we may prove ( the converse of Thirdly ) that of two unequal oblique lines , AD and AE 3 BOOK I. 33.
... be greater or less than AE ; but both of these results are contrary to the hypothesis ; therefore , BC = BE . COR . 4. In like manner , we may prove ( the converse of Thirdly ) that of two unequal oblique lines , AD and AE 3 BOOK I. 33.
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, After Legendre: With a Selection of Geometrical ... Charles Scott Venable Προβολή αποσπασμάτων - 1890 |
Elements of Geometry, After Legendre: With a Selection of Geometrical ... Adrien Marie Legendre,Charles Scott Venable Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2014 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ACB angles equal apothem base bisect bisectrix Book centre chord circ circumference circumscribed circle common cone Construct convex surface cylinder decagon described diagonals diameter dicular diedral distance divided draw drawn edges equally distant equilateral triangle equivalent Exercises exterior angles Find the locus frustum Geometric given circle given line given point given straight line greater Hence homologous homologous sides hypothenuse isosceles join let fall line parallel loci measure median meet middle point number of sides opposite parallelogram parallelopipedon perimeter perpen perpendicular plane angles plane MN point of contact point of intersection polyedron prism problem Prop proportional PROPOSITION pyramid quadrilateral radii ratio rectangle regular polygon right angled triangle S-ABC SCHOLIUM segment similar solid angle sphere spherical triangle square tangent tetraedron THEOREM triangle ABC triangular prism triedral vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 255 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Σελίδα 49 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Σελίδα 20 - Parallel straight lines are such as are in the same plane, and which, being produced ever so far both ways, do not meet.
Σελίδα 54 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Σελίδα 45 - 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 67 - 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 107 - 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 300 - The volume of a frustum of a cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the bases of the frustum.
Σελίδα 276 - Scholium. The spherical ungula, bounded by the planes AMB, ANB, is to the whole solid sphere, as the angle A is to four right angles. For, the lunes being equal, the spherical ungulas will also be equal ; hence two spherical ungulas are to each other, as the angles formed by the planes which bound them. PROPOSITION XVIII.
Σελίδα 9 - Ratio is the relation which one quantity bears to another in respect of magnitude, the comparison being made by considering what multiple, part, or parts, one is of the other.