The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1 |
From inside the book
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Page 40
... defn ( Def . 35 ) of parallel straight lines , AB is parallel to CD . And the same thing might have been shewn , if EF had made the other pair of alternate angles вGH , GHC equal . Hence , if EF cutting the two straight 40 [ воок THE ...
... defn ( Def . 35 ) of parallel straight lines , AB is parallel to CD . And the same thing might have been shewn , if EF had made the other pair of alternate angles вGH , GHC equal . Hence , if EF cutting the two straight 40 [ воок THE ...
Page 86
... defn of a circle . But because the angle нCK is adjacent to the right angle BCE , and therefore a right angle ( Def . 10 ) , the squares of HC , CK are likewise equal ( i . 47 ) to the square of HK ; and things that are equal to the ...
... defn of a circle . But because the angle нCK is adjacent to the right angle BCE , and therefore a right angle ( Def . 10 ) , the squares of HC , CK are likewise equal ( i . 47 ) to the square of HK ; and things that are equal to the ...
Page 87
... defn nor an axiom , but consists of two props which may be thus proved . ( 1 ) Let ABC , DEF be two circles , of which the centres are G , H , and which have equal radii . Then the circle ABC shall be equal to the circle DEF , and the ...
... defn nor an axiom , but consists of two props which may be thus proved . ( 1 ) Let ABC , DEF be two circles , of which the centres are G , H , and which have equal radii . Then the circle ABC shall be equal to the circle DEF , and the ...
Page 91
... defn each of these angles is a right angle . But FDB is likewise a right angle by const ; and all right angles are equal ( Ax . 11 ) ; there- fore the angle HDB is equal to the angle FDB , that is , the part.equal to the whole : which ...
... defn each of these angles is a right angle . But FDB is likewise a right angle by const ; and all right angles are equal ( Ax . 11 ) ; there- fore the angle HDB is equal to the angle FDB , that is , the part.equal to the whole : which ...
Page 100
... defn of a circle MK is equal to MB , and MD is common to the two triangles DMK , DMB : therefore these two triangles have the two sides KM , MD equal to the two sides BM , MD respectively , and the included angle KMD is equal to the ...
... defn of a circle MK is equal to MB , and MD is common to the two triangles DMK , DMB : therefore these two triangles have the two sides KM , MD equal to the two sides BM , MD respectively , and the included angle KMD is equal to the ...
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.