Euclid for beginners, books i. and ii., with simple exercises by F.B. HarveyLongmans, Green, and Company, 1880 - 119 sider |
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Side 44
... angle equal to the interior and opposite angle on the same side of the line ; or make the two interior angles on the ... AGH ( I. 15 ) , therefore the angle AGH the angle GHD ( ax . 1 ) ; and these are alternate angles . Therefore , it ...
... angle equal to the interior and opposite angle on the same side of the line ; or make the two interior angles on the ... AGH ( I. 15 ) , therefore the angle AGH the angle GHD ( ax . 1 ) ; and these are alternate angles . Therefore , it ...
Side 45
... angles on the left of the cutting line EF , viz . the exterior angle EGA = the interior and opposite angle GHC , and the two interior angles AGH and GHC . 2. If any angle BAC be bisected by a straight line AD , and any point E be taken ...
... angles on the left of the cutting line EF , viz . the exterior angle EGA = the interior and opposite angle GHC , and the two interior angles AGH and GHC . 2. If any angle BAC be bisected by a straight line AD , and any point E be taken ...
Side 46
... angle AGH GHD . = the alternate angle 2. The exterior angle EGB = the interior and opposite angle GHD . 3. The two interior angles BGH and GHD = two right angles . C E G B H PROOF . - 1 . If the angle AGH is not equal to the angle GHD ...
... angle AGH GHD . = the alternate angle 2. The exterior angle EGB = the interior and opposite angle GHD . 3. The two interior angles BGH and GHD = two right angles . C E G B H PROOF . - 1 . If the angle AGH is not equal to the angle GHD ...
Side 47
... angle AGH is greater than the angle GHD is erroneous . Similarly , the supposition that the angle AGH is less than the angle GHD might be shewn to be erroneous . Consequently , the angle AGH the angle GHD . Therefore , it is proved , as ...
... angle AGH is greater than the angle GHD is erroneous . Similarly , the supposition that the angle AGH is less than the angle GHD might be shewn to be erroneous . Consequently , the angle AGH the angle GHD . Therefore , it is proved , as ...
Side 48
... angle GHF ; therefore the angle AGH = the angle HKD , i.e. the angle AGK = the angle GKD ( note 2 def . 15 ) ; and these are alternate angles . Therefore , it is proved , as required , that The straight lines AB and CD are parallel ( I ...
... angle GHF ; therefore the angle AGH = the angle HKD , i.e. the angle AGK = the angle GKD ( note 2 def . 15 ) ; and these are alternate angles . Therefore , it is proved , as required , that The straight lines AB and CD are parallel ( I ...
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Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey Euclides,Frederick Burn Harvey Uten tilgangsbegrensning - 1880 |
Euclid for Beginners, Books I. and II., with Simple Exercises by F.B. Harvey Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABCD AC and CD alternate angle angle ABC angle ACB angle AGH angle BAC Arithmetic base BC Beginners bisected Book centre circle coincides cons Construction CONSTRUCTION.-1 crown 8vo describe Dictionary divided double the square draw drawn Edition Elementary English equal Euclid Exercises exterior angle falls figure former four French Geography German given straight line gnomon greater Greek half History join Language Latin latter less Lessons Let ABC London LONGMANS Manual Maps meet Notes opposite angle parallel parallelogram Plane post 8vo PROBLEM produced proof PROOF.-Because PROP Proposition proved Reader Reading rect rectangle contained rectilineal right angles School Second side AC Similarly small 8vo square on AC Standard Stepping-Stone straight line supposition THEOREM third translated triangle ABC vols Wherefore whole
Populære avsnitt
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.