The Teaching of GeometryGinn, 1911 - 339 sider |
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Side 137
... illustration of line as " the edge of a shadow , " thus making it real but not material . Aristotle speaks of a line as a magnitude " divisible in one way only , " as con- trasted with a surface which is divisible in two ways , and with ...
... illustration of line as " the edge of a shadow , " thus making it real but not material . Aristotle speaks of a line as a magnitude " divisible in one way only , " as con- trasted with a surface which is divisible in two ways , and with ...
Side 140
... illustrations . The shadow cast on a table top is a good illustration , since all idea of thickness is wanting . It adds to the understanding of the concept to introduce Aristotle's statement that a sur- face is generated by a moving ...
... illustrations . The shadow cast on a table top is a good illustration , since all idea of thickness is wanting . It adds to the understanding of the concept to introduce Aristotle's statement that a sur- face is generated by a moving ...
Side 169
... illustrations of this theorem . Indeed , any two crossed lines , as in a pair of shears or the legs of a camp stool , bring it to mind . The word " straight " is here omitted before " lines " in accordance with the modern convention ...
... illustrations of this theorem . Indeed , any two crossed lines , as in a pair of shears or the legs of a camp stool , bring it to mind . The word " straight " is here omitted before " lines " in accordance with the modern convention ...
Side 172
... illustration of the method is seen in Belli's work of 1569 , as here shown . At the top of the picture a man is getting the angle by means of the visor of his cap ; at the bottom of the picture a man is using a ruler screwed to a staff ...
... illustration of the method is seen in Belli's work of 1569 , as here shown . At the top of the picture a man is getting the angle by means of the visor of his cap ; at the bottom of the picture a man is using a ruler screwed to a staff ...
Side 179
... illustration here given shows how this form of level was used three hundred years ago . Teachers who seek for geometric figures in practical mechanics will find this proposition illustrated in the ordinary hoisting apparatus of the kind ...
... illustration here given shows how this form of level was used three hundred years ago . Teachers who seek for geometric figures in practical mechanics will find this proposition illustrated in the ordinary hoisting apparatus of the kind ...
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Vanlige uttrykk og setninger
algebra altitude ancient angles are equal applications Archimedes Aristotle axioms basal base beginning bisect Book called century A.D. CHAPTER circle circumference congruent considered construction corollary cube curve cylinder define definition distance drawing easily edge educational elementary geometry etry Euclid Euclid's Elements example exercises fact figure geom given line Greek Heron of Alexandria hexagon illustration incommensurable inscribed interest intersect isosceles locus logic mathematician mathematics means measure method modern octahedron parallel parallelepiped parallelogram perpendicular plane geometry Plato polyhedrons postulate practical prism problem Proclus proof proportion proposition proved pupil pyramid Pythagoras Pythagorean Theorem question radius ratio reason regular polygons relating right angles right triangle segment sides solid geometry sphere square straight line surface syllabus tangent teacher teaching of geometry textbook Thales thing tion to-day trigonometry usually vertex vertices volume words writers
Populære avsnitt
Side 254 - Two triangles having 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.
Side 182 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Side 125 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Side 143 - A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another; 16 And the point is called the center of the circle.
Side 188 - 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.
Side 145 - ... 20. Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal.
Side 244 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Side 225 - Magnitudes are said to have a ratio to one another which are capable, when multiplied, of exceeding one another.
Side 142 - But when a straight line, standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a right angle, and the straight line which stands on the other is called a perpendicular to it (Def.
Side 54 - Euclid's, and show by construction that its truth was known to us ; to demonstrate, for example, that the angles at the base of an isosceles triangle are equal...