Syllabus of Plane Geometry: (corresponding to Euclid, Book I-VI) ; Prepared as an Introduction to Absolute GeometryStandard Press, 1905 - 42 σελίδες |
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Συχνά εμφανιζόμενοι όροι και φράσεις
A:B is called adjacent angles angles are equal angles formed antecedent base and altitude called a ratio circle is divided CORA corresponding angles corresponding sides proportional diagonal equal altitudes equal angles equal arcs equal bases equal chords equal circles equal respectively equal sides Euclid exterior ference four magnitudes given point given straight line greater angle greater ratio greater side hyperbolic space hypote hypotemuse inscribed angle interior angles intersection isosceles triangle joining their centers lines is called magni middle point minor arcs multiples opposite sides pair of equal parallelogram parallels are equal perigon perpendicular PLANE GEOMETRY polygon formed postulate Prop quadrilateral radius ratio A:B ratio are equal right angle right-angled triangle second ratio SECTION sectors segment Similar polygons Similar triangles space-form squares straight angle straight line cuts straight line drawn surface SYLLABUS OF PLANE tangent Theor theorems third side transversal triangle is equal triangles are congruent tude vertex
Δημοφιλή αποσπάσματα
Σελίδα 26 - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.
Σελίδα 27 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Σελίδα 15 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Σελίδα 41 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 26 - ... less than the sum of the other two sides of the triangle.
Σελίδα 36 - Equal triangles, on equal bases, in the same straight line, and on the same side of it, are between the same parallels.
Σελίδα 23 - MAGNITUDES which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the same ratio are equal to one another.
Σελίδα 35 - 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.
Σελίδα 33 - Any exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Σελίδα 38 - The sum of the squares on the sides of a quadrilateral is...