The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1 |
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Page 13
... def " ( Def . 15 ) . But by construction the straight line c is equal to AD ; and things that are equal to the same ... angle included by the two sides of the one equal to the angle included by the two sides of the other : then these ...
... def " ( Def . 15 ) . But by construction the straight line c is equal to AD ; and things that are equal to the same ... angle included by the two sides of the one equal to the angle included by the two sides of the other : then these ...
Page 14
... DEF . Let the triangle ABC be applied to the triangle DEF , so that the point A may coincide with the point D , and ... angle BAC is equal to the angle EDF by hyps ; and the triangles fall by const " on the same side of DE : hence also ...
... DEF . Let the triangle ABC be applied to the triangle DEF , so that the point A may coincide with the point D , and ... angle BAC is equal to the angle EDF by hyps ; and the triangles fall by const " on the same side of DE : hence also ...
Page 18
... angle BDC is equal to the angle BCD ; but it has been shewn to be greater than it which is im- possible . A B II . Let the vertex of one of the triangles , as D , be within the other triangle , ACB . D E F Join CD ; and produce AC , AD ...
... angle BDC is equal to the angle BCD ; but it has been shewn to be greater than it which is im- possible . A B II . Let the vertex of one of the triangles , as D , be within the other triangle , ACB . D E F Join CD ; and produce AC , AD ...
Page 20
... DEF . A B D F E Let the triangle ABC be applied to the triangle DEF , so that the point A may coincide with the ... angle , i . e . to divide it into two equal angles . Let BAC be the given angle . It is required to bisect the angle ABC ...
... DEF . A B D F E Let the triangle ABC be applied to the triangle DEF , so that the point A may coincide with the ... angle , i . e . to divide it into two equal angles . Let BAC be the given angle . It is required to bisect the angle ABC ...
Page 21
... angle BAC shall be bisected by the straight line AF . B D F E Because AD is equal to AE by const " , and DF is equal to EF , since they are sides of the equilateral triangle DEF , and AF is common to the two triangles ADF , AEF ...
... angle BAC shall be bisected by the straight line AF . B D F E Because AD is equal to AE by const " , and DF is equal to EF , since they are sides of the equilateral triangle DEF , and AF is common to the two triangles ADF , AEF ...
Common terms and phrases
ABC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles are equal angular points base BC bisected centre circle ABC circle DEF circumference const cut the circle diagonal draw equal angles equal Ax equals add equi equimultiples exterior angle FGHKL fore four magnitudes fourth given straight line gnomon hence the angle homologous hyps included angle interior and opposite join less Let ABC multiple opposite angle parallelogram perpendicular produced PROP proportional proved radius rectangle contained remaining angle respectively equal right angles segment shewn sides BC similar solid angle square of AC THEOR thing are equal third angle three angles touching the circle triangle ABC unequal
Popular passages
Page 39 - 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...
Page 52 - 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.
Page 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Page 5 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw, from the point A, a straight line equal to BC.
Page 11 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.
Page 105 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Page 118 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Page 66 - 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.
Page 6 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Page 119 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.