Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes; together with a selection of geometrical exercises. To which is prefixed an intr., containing a brief outline of the history of geometry. By R. Potts. [With] Appendix1845 |
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Side vi
... isosceles right - angled triangle , and observing that the sum of the two lunes , between the two quadrants of the larger semicircle and the two smaller semicircles , was equal to the area of the triangle . By means of the lunes he ...
... isosceles right - angled triangle , and observing that the sum of the two lunes , between the two quadrants of the larger semicircle and the two smaller semicircles , was equal to the area of the triangle . By means of the lunes he ...
Side 3
... Of three - sided figures , an equilateral triangle is that which has three equal sides . XXV . An isosceles triangle is that which has two sides equal . XXVI . A scalene triangle is that which has three 1-2 DEFINITIONS . 3.
... Of three - sided figures , an equilateral triangle is that which has three equal sides . XXV . An isosceles triangle is that which has two sides equal . XXVI . A scalene triangle is that which has three 1-2 DEFINITIONS . 3.
Side 9
... isosceles triangle are equal to each other ; and if the equal sides be produced , the angles on the other side of the base shall be equal . Let ABC be an isosceles triangle of which the side AB is equal to AC , and let the equal sides ...
... isosceles triangle are equal to each other ; and if the equal sides be produced , the angles on the other side of the base shall be equal . Let ABC be an isosceles triangle of which the side AB is equal to AC , and let the equal sides ...
Side 43
... isosceles triangle , the word only must be omitted , as the equilateral triangle is considered isosceles in Prop . 15 , Book Iv . Objection has been made to the definition of an acute - angled triangle . It is said that it cannot be ...
... isosceles triangle , the word only must be omitted , as the equilateral triangle is considered isosceles in Prop . 15 , Book Iv . Objection has been made to the definition of an acute - angled triangle . It is said that it cannot be ...
Side 49
... isosceles triangle . It would , however , be less general than Euclid's . Prop . XXIV . Simson makes the angle EDG at D in the line ED , the side which is not the greater of the two ED , DF ; otherwise , three different cases would ...
... isosceles triangle . It would , however , be less general than Euclid's . Prop . XXIV . Simson makes the angle EDG at D in the line ED , the side which is not the greater of the two ED , DF ; otherwise , three different cases would ...
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Euclid's Elements of Geometry [Book 1-6, 11,12] with Explanatory Notes ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
AC is equal altitude angle ABC angle BAC angle equal base BC chord circle ABCD circumference cone cylinder describe a circle diagonals diameter divided draw EFGH equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements Geometry given angle given circle given line given point given straight line given triangle gnomon greater hypothenuse inscribed interior angles intersection isosceles triangle less Let ABC lines be drawn magnitudes meet the circumference multiple opposite sides parallel parallelogram pentagon perpendicular polygon prism problem Proclus produced Prop proportional proved pyramid Q.E.D. PROPOSITION radius rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar triangles solid angle solid parallelopipeds square of AC tangent THEOREM touches the circle trapezium triangle ABC vertex vertical angle wherefore
Populære avsnitt
Side 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Side 29 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Side 26 - Wherefore, if a straight line, &c. QED PROPOSITION XXIX. THEOREM. Jf a straight line fall upon two parallel straight lines, it makes the alternate angles equal...
Side 99 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Side 15 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...
Side 58 - If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 22 - IF two triangles have two sides of the one equal to two sides of the...
Side vi - The sluggard is wiser in his own conceit than seven men that can render a reason.
Side 54 - If there be imo straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 26 - 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.