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 TrigonometryMarot & Walter, 1826 - 320 σελίδες |
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Σελίδα xv
... angle , nor that the equal sides are opposite to equal angles ; nor , lastly , that things equal to the same thing are equal to one another ? By a scientific mind , this information will not be thought lightly of ; and it is exactly ...
... angle , nor that the equal sides are opposite to equal angles ; nor , lastly , that things equal to the same thing are equal to one another ? By a scientific mind , this information will not be thought lightly of ; and it is exactly ...
Σελίδα 26
... equal to C the less . Which was to be done . N. PROP . IV . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another ...
... equal to C the less . Which was to be done . N. PROP . IV . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another ...
Σελίδα 27
... equal , and the remaining angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two triangles have two ...
... equal , and the remaining angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two triangles have two ...
Σελίδα 28
... equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal , and their remaining angles are equal , to which the equal sides are opposite ; therefore the an- gle ...
... equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal , and their remaining angles are equal , to which the equal sides are opposite ; therefore the an- gle ...
Σελίδα 29
... equal to one another , and likewise those which are terminated in the other extre- mity , equal to one another . Let ... angles ECD , FDC upon the other side of the base a A E F B CD are equal to one another , but the angle ECD is ...
... equal to one another , and likewise those which are terminated in the other extre- mity , equal to one another . Let ... angles ECD , FDC upon the other side of the base a A E F B CD are equal to one another , but the angle ECD is ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry: Containing the First Six Books of Euclid; With Two ... Formerly Chairman Department of Immunology John Playfair Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected Book centre circle ABC circumference cosine cylinder demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line gles greater hypotenuse inscribed join less Let ABC line BC magnitudes meet opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB proportional proposition pyramid Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle right angled triangle segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line AC Supplement THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 233 - But because the triangle KGN is isosceles, the angle GKN is equal to the angle GNK, and the angles GMK, GMN are both right angles by construction ; wherefore, the triangles GMK, GMN have two angles of the one equal to two angles of the other, and they have also the side GM common, therefore they
Σελίδα 18 - 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. VIII. An obtuse angle is that which is greater than a right angle.
Σελίδα 77 - AB is divided in H, so that the rectangle AB, BH is equal to the square of AH. Let AB be the given straight line; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal
Σελίδα 69 - 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. Let the straight line AB be divided into two equal parts in the
Σελίδα 48 - PROP. XXX. THEOR. Straight lines which are parallel to the same straight line are parallel to one another. Let AB, CD, be each of them parallel to EF; AB is also parallel to CD. Let the straight line GHK cut AB, EF, CD ; and because GHK cuts the parallel straight lines
Σελίδα 32 - PROP. XI. PROB. To draw a straight line at right angles to a given straight line, from a given point in that line. Let AB be a given straight line, and Ca point given in it; it is required to draw a straight line from the point C at right angles to AB.
Σελίδα 75 - PROP. X. THEOR. If a straight line be bisected, and produced to any point, the square* of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half
Σελίδα 18 - taken, the straight line between them lies wholly in that superficies. VI. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line. E NB ' When several angles are at one point B, any one of them is
Σελίδα 153 - Therefore, &c. QED PROP. IV. THEOR. If the first of four magnitudes has the same ratio to the second which the third has to the fourth, and if any equimultiples whatever be taken of the first and third, and any whatever of the second and fourth; the multiple
Σελίδα 50 - angles. Therefore, twice as many right angles as the figure has sides, are equal to all the angles of the figure, together with four right angles, that is, the angles of the figure are equal to twice as many right angles as the figure has sides, wanting four. Because every interior angle ABC, with its adjacent exterior ABD, is