## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes; together with a selection of geometrical exercises. To which is prefixed an intr., containing a brief outline of the history of geometry. By R. Potts. [With] Appendix |

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Page vi

80 17 equal

80 17 equal

**less less**equal . 111 5 ABC ACB . 3--2 3-2 125 23 3 .. INTRODUCTION . The aim of the following brief notices ,. 3 172 In the diagram , Prop . Page 8

From the greater of two given straight lines to cut off a part equal to the

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 , of which AB is the greater ... Page 18

Any two angles of a triangle are together

Any two angles of a triangle are together

**less**than two right angles . Let ABC be any triangle . Then any two of its angles together shall be**less**than two ... Page 19

Again , if AC were

Again , if AC were

**less**than AB , then the angle ABC would be**less**than the ... but it is not**less**, therefore the side AC is not**less**than AB ; and AC has ... Page 20

Then BD and DC shall be

Then BD and DC shall be

**less**than BA and AC the other two sides of the triangle , but shall contain an angle BDC greater than the angle BAC .### What people are saying - Write a review

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Euclid's Elements of Geometry [Book 1-6, 11,12] with Explanatory Notes ... Euclides No preview available - 2016 |

### Common terms and phrases

altitude base bisected Book centre chord circle circle ABCD circumference common cone construction cylinder definition demonstrated described diagonals diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid extremities fall figure formed four fourth Geometry given circle given line given point given straight line greater half Hence inscribed intersection join less line drawn magnitudes manner means meet multiple opposite sides parallel parallelogram pass perpendicular plane polygon position problem produced Prop properties proportional PROPOSITION proved pyramid radius ratio reason rectangle contained regular remaining respectively right angles segment semicircle shew shewn sides similar solid sphere square straight line taken tangent THEOREM third touch triangle ABC twice vertex vertical wherefore whole

### Popular passages

Page 56 - 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 29 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.

Page 26 - Wherefore, if a straight line, &c. QED PROPOSITION XXIX. THEOREM. Jf a straight line fall upon two parallel straight lines, it makes the alternate angles equal...

Page 99 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.

Page 15 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...

Page 60 - If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

Page 22 - IF two triangles have two sides of the one equal to two sides of the...

Page vi - The sluggard is wiser in his own conceit than seven men that can render a reason.

Page 54 - If there be imo straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 26 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.