## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

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DEFINITIONS . a I. A point is that which hath no parts , or which hath no

DEFINITIONS . a I. A point is that which hath no parts , or which hath no

**magnitude**. II . A line is length without breadth . III . The extremities of a line are points . iv . A straight line is that which lies evenly between its ... Page 126

I. A less

I. A less

**magnitude**is said to be a part of a greater**magnitude**when the less measures the greater ; that is , ' when the ... “ Ratio a mutual relation of two**magnitudes**“ of the same kind to one another , in respect • of quantity . Page 127

V. The first of four

V. The first of four

**magnitudes**is said to have the same ratio to the second , which the third has to the fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and ... Page 128

X. When three

X. When three

**magnitudes**are proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI . When four**magnitudes**are continual proportionals , the first is said to have to the fourth ... Page 129

Geometers make use of the following technical ' words , to signify certain ways of changing • either the order or

Geometers make use of the following technical ' words , to signify certain ways of changing • either the order or

**magnitude**of propor• tionals , so that they continue still to be proportionals . ' XIII . Permutando , or alternando , by ...### What people are saying - Write a review

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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |

### Common terms and phrases

altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole