Euclid for beginners, books i. and ii., with simple exercises by F.B. HarveyLongmans, Green, and Company, 1880 - 119 sider |
Fra bogen
Resultater 1-5 af 27
Side 4
... side AB on the side DE , then , because AB = DE ( hyp . ) ,. therefore the point B shall coincide with the point E , and the side AB shall coincide with the side DE . Next , because the side AB coincides with the side DE , and because ...
... side AB on the side DE , then , because AB = DE ( hyp . ) ,. therefore the point B shall coincide with the point E , and the side AB shall coincide with the side DE . Next , because the side AB coincides with the side DE , and because ...
Side 6
... side of the base are also equal to each other . Let ABC be an isosceles triangle with the side AB = the side AC , and let AB and AC be produced to D and E respectively . Then it is to be proved that 1. The angles ABC and ACB , at the ...
... side of the base are also equal to each other . Let ABC be an isosceles triangle with the side AB = the side AC , and let AB and AC be produced to D and E respectively . Then it is to be proved that 1. The angles ABC and ACB , at the ...
Side 8
... side AB = the side AC . B D CONSTRUCTION . Suppose that AB is greater than AC . --- From AB cut off a part DB = AC ( I. 3 ) and join CD . PROOF . - Because in the triangles DBC and ACB we have the sides DB and BC and their angle DBC ...
... side AB = the side AC . B D CONSTRUCTION . Suppose that AB is greater than AC . --- From AB cut off a part DB = AC ( I. 3 ) and join CD . PROOF . - Because in the triangles DBC and ACB we have the sides DB and BC and their angle DBC ...
Side 9
... side AB the side AC . If two angles of a triangle , & c . Q. E. D. Cor . - Every equiangular triangle is also equilateral . N.B. - The proof here given is an instance of what is called Indirect Demonstration . This means , the truth of ...
... side AB the side AC . If two angles of a triangle , & c . Q. E. D. Cor . - Every equiangular triangle is also equilateral . N.B. - The proof here given is an instance of what is called Indirect Demonstration . This means , the truth of ...
Side 10
... AB , and on the same side of it - e.g . above it - there can be two triangles , ACB and ADB , having the sides AC and AD terminated in one extremity of the base , A , = each other , and having also the sides BC and BD terminated in the ...
... AB , and on the same side of it - e.g . above it - there can be two triangles , ACB and ADB , having the sides AC and AD terminated in one extremity of the base , A , = each other , and having also the sides BC and BD terminated in the ...
Andre udgaver - Se alle
Euclid for Beginners, Books I. and II., with Simple Exercises by F.B. Harvey Euclides Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
ABC and ABD AC and CD adjacent angles alternate angle angle ABC angle ACB angle AGH angle BAC angle CEB angle DEF angle EDF angle GHD Arithmetic BA and AC base BC Beginners bisected CONSTRUCTION.-1 crown 8vo Dictionary double the square draw Edition English Grammar English History equilateral Euclid exterior angle Gallic War Geography given straight line gnomon greater Greek half a right i.e. the angle interior and opposite join Latin Let ABC line be divided LONGMANS Manual note 2 def opposite angle parallel parallelogram post 8vo produced PROOF.-Because Proposition proved Q. E. D. Exercise Q. E. D. PROP rectangle contained rectilineal figure right angles School side AB side AC small 8vo square on AC Stepping-Stone straight line CD THEOREM triangle ABC twice the rect twice the rectangle vols Wherefore
Populære passager
Side 48 - 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 88 - 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 on the line between the points of section, is equal to the square on half the line.
Side 14 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Side 36 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Side 64 - 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.
Side 108 - In every triangle, the square on the side subtending an acute angle, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B an acute angle; and on BC one of the sides containing it, let fall the perpendicular...
Side 47 - 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.
Side 104 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Side 52 - 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 20 - If, at a point in a straight line, two other straight lines upon the opposite sides of it, make the adjacent angles, together equal to two right angles, these two straight lines shall be in one and the same straight line.