Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids : to which are Added Elements of Plane and Spherical TrigonometryW.E. Dean, 1853 - 317 σελίδες |
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Αποτελέσματα 1 - 5 από τα 47.
Σελίδα 3
... fall to the share either of himself , or of any other of the moderns . But , after all this was accomplished , something still remained to be done , since , notwithstanding the acknowledged excellence of EUCLID's Ele- ments , it could ...
... fall to the share either of himself , or of any other of the moderns . But , after all this was accomplished , something still remained to be done , since , notwithstanding the acknowledged excellence of EUCLID's Ele- ments , it could ...
Σελίδα 27
... falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines are parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF ...
... falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines are parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF ...
Σελίδα 28
... fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together ...
... fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together ...
Σελίδα 30
... falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC , but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite ...
... falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC , but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite ...
Σελίδα 38
... falls upon the parallels AH , EF , the angles AHF , HFE , are together equal ( 29. 1. ) to two right angles ; wherefore the angles BHF , HFE are less than two right angles ; But straight lines which with another straight line make the ...
... falls upon the parallels AH , EF , the angles AHF , HFE , are together equal ( 29. 1. ) to two right angles ; wherefore the angles BHF , HFE are less than two right angles ; But straight lines which with another straight line make the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 51 - 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.
Σελίδα 74 - THE angles in the same segment of a circle are equal to one another...
Σελίδα 37 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 29 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Σελίδα 29 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through EAF the point A, parallel to the straight line '
Σελίδα 147 - If the vertical angle of a triangle be bisected by a straight line which also cute 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.
Σελίδα 19 - The angles which one straight line makes with another upon one side of i't, are either two right angles, or are together eqval to two right angles.
Σελίδα 134 - IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean : and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.
Σελίδα 294 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 13 - BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.