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 53
... half of the parallelogram GBCA : and since DC is one of the diagonals of the parallelogram DBCH , it bisects it , and therefore the triangle DBC is half of the parallelogram DBCH . But the parallelograms GBCA , DBCH were shewn to be ...
... half of the parallelogram GBCA : and since DC is one of the diagonals of the parallelogram DBCH , it bisects it , and therefore the triangle DBC is half of the parallelogram DBCH . But the parallelograms GBCA , DBCH were shewn to be ...
Page 54
... half of KBCA ; and since DF is one of the diagonals of the parallelogram DEFL , it bisects it , and the triangle DEF is half of DEFL . But KBCA , DEFL were shewn to be equal ; and the halves of equal things are equal ( Ax . 7 ) ...
... half of KBCA ; and since DF is one of the diagonals of the parallelogram DEFL , it bisects it , and the triangle DEF is half of DEFL . But KBCA , DEFL were shewn to be equal ; and the halves of equal things are equal ( Ax . 7 ) ...
Page 72
... half the line . Let the straight line AB be bisected in c , and divided into two unequal parts in D. Then the rectangle AD , DB together with the square of CD shall be equal to the square of BC . On CB describe ( i . 46 ) the square ...
... half the line . Let the straight line AB be bisected in c , and divided into two unequal parts in D. Then the rectangle AD , DB together with the square of CD shall be equal to the square of BC . On CB describe ( i . 46 ) the square ...
Page 74
... half the bisected line , shall be equal to the square of the line , which is made up of the half and the part produced . Let the straight line AB be bisected in c and produced Then the rectangle AD , DB together with the square of CB ...
... half the bisected line , shall be equal to the square of the line , which is made up of the half and the part produced . Let the straight line AB be bisected in c and produced Then the rectangle AD , DB together with the square of CB ...
Page 78
... half the line , and the square of the line between the points of section . E F Let the straight line AB be bisected in c and divided into two unequal parts AD , DB in D. Then the squares of AD , DB shall be double of the squares of AC ...
... half the line , and the square of the line between the points of section . E F Let the straight line AB be bisected in c and divided into two unequal parts AD , DB in D. Then the squares of AD , DB shall be double of the squares of AC ...
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.