First Lessons in Geometry Upon the Model of Colburn's First Lessons in ArithmeticD. Appleton and Company, 1859 |
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Σελίδα 12
... bisect a Line To draw Perpendiculars and Parallels To describe and bisect Angles To describe Triangles and Parallelograms To trisect a Right Angle PART IV . Measure of Surface . 122 122 124 125 129 Comparison of Parallelograms and ...
... bisect a Line To draw Perpendiculars and Parallels To describe and bisect Angles To describe Triangles and Parallelograms To trisect a Right Angle PART IV . Measure of Surface . 122 122 124 125 129 Comparison of Parallelograms and ...
Σελίδα 95
... bisecting aA . Then , as the triangles ABD and ACD have AB = AC , aBAD = aCAD , and the side AD common , tABD≈ tACD ? aBaC ? § 70. II . Given , in tABC , Required , aB B XXVI . A 40 . 40. R. XXVII . A AC > AB . aC . D In AC , take AD ...
... bisecting aA . Then , as the triangles ABD and ACD have AB = AC , aBAD = aCAD , and the side AD common , tABD≈ tACD ? aBaC ? § 70. II . Given , in tABC , Required , aB B XXVI . A 40 . 40. R. XXVII . A AC > AB . aC . D In AC , take AD ...
Σελίδα 98
... bisecting the angle at the vertex of an isosceles triangle is perpendicular to the base and bisects it . PROPOSITION X. § 77. Given , any triangle ABC . Required , any one side ≈≈≈ the sum of the other two . B XXXI . A C Let BC be ...
... bisecting the angle at the vertex of an isosceles triangle is perpendicular to the base and bisects it . PROPOSITION X. § 77. Given , any triangle ABC . Required , any one side ≈≈≈ the sum of the other two . B XXXI . A C Let BC be ...
Σελίδα 103
... bisect the second at right angles . g . ) Hence , if one straight line passes through the middle of a second , and any other point of the first is equally distant from the extremities of the second , what angles do the two lines make ...
... bisect the second at right angles . g . ) Hence , if one straight line passes through the middle of a second , and any other point of the first is equally distant from the extremities of the second , what angles do the two lines make ...
Σελίδα 118
... quadrilateral ABCD , the diag- onals AC and BD bisecting each other in O. D XLV . B ( w ) Lat . , upper . ( x ) Lat . , lower . ( y ) L. altitudo , height . с Required , AB DC , and AD BC . What 118 PART II . [ § 125 , 126 . GEOMETRY .
... quadrilateral ABCD , the diag- onals AC and BD bisecting each other in O. D XLV . B ( w ) Lat . , upper . ( x ) Lat . , lower . ( y ) L. altitudo , height . с Required , AB DC , and AD BC . What 118 PART II . [ § 125 , 126 . GEOMETRY .
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Συχνά εμφανιζόμενοι όροι και φράσεις
AB² aBAC ABCD AC² adjacent angles altitude angle ABC angles equal angular points Arithmetic base and altitude BC² bend bisect breadth broken line centre contain curve describe arcs cutting diagonal diedral angles difference dimensions direction distance distinct straight lines divergence divided draw equal angles equiangular polygons equilateral exterior fall figure GEOM Geometry given angle greater hypotenuse identical triangles inches interior angles isosceles triangle Join lelogram length less Let AC line drawn magnitudes Mary Howitt multiplied oblique obtuse paral parallel parallelogram perpendicular plane polygon PROBLEM produced PROPOSITION quadrilateral radius reckoned rectangle Required RHOMBUS right angles right triangle rods Show solid angles subtending subtract surface tABC tABD termed THEOR theorem triangle ABC Triangles agreeing unequal vertex vols zoid
Δημοφιλή αποσπάσματα
Σελίδα 18 - In the mathematics I can report no deficience, except it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For, if the wit be too dull, they sharpen it ; if too wandering, they fix it ; if too inherent in the sense, they abstract it.
Σελίδα 123 - Most good practical workmen have several means for getting the cut of the mitre, and to them this demonstration will appear unnecessary, but I have seen many men make sad blunders, for want of knowing this simple rule. PROBLEM 12.
Σελίδα 22 - A 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 93 - Any exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Σελίδα 147 - In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Σελίδα 21 - ... that the angle inscribed in a semicircle is a right angle, and to have testified his joy by a sacrifice to the Muses!
Σελίδα 154 - Side subtending the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle.
Σελίδα 97 - The difference between any two sides of a triangle is less than the third side.
Σελίδα 23 - Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles.
Σελίδα 24 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.