## The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendix |

### From inside the book

Results 6-10 of 33

Page 54

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**rectangle contained**by AD , DB , for DH is equal * to DB ; and DF , together with CH , is the gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : to each of these equals add LG , which is equal to the square of CD ... Page 55

... rectangle AL is equal * to CH ; but CH is equal * to HF ; there- K fore AL is also equal to HF : to each of these equals add CM ; therefore the whole AM is 4. 2 . equal to the gnomon CMG : but AM is the

... rectangle AL is equal * to CH ; but CH is equal * to HF ; there- K fore AL is also equal to HF : to each of these equals add CM ; therefore the whole AM is 4. 2 . equal to the gnomon CMG : but AM is the

**rectangle contained**by AD , DB ... Page 56

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**rectangle**AB , BC is double of AK , for BK is equal * to BC : therefore the gnomon AKF , together with the square CK ...**contained**by the whole line , and one of the parts , together with the square of the other part , is equal to ... Page 57

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**rectangle**CK is equal * to BN , * 36. 1 . and GR to RN : but CK is equal to RN , because * 43. 1 . they are the ...**contained**by AB , BC , for BK has been proved equal to BC ; therefore four times the rect- angle AB , BC is ... Page 61

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**rectangle contained**by the whole and one of the parts , shall be equal to the square of the other part . Let AB be the given straight line ; it is required to divide it into two parts , so that the**rectangle contained**by the whole ...### Other editions - View all

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |

### Common terms and phrases

AB is equal AC is equal altitude angle ABC angle ACB angle BAC base BC bisect centre circle ABCD circle EFGH circumference common section cone cylinder demonstrated described diameter draw equal to F equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prisms PROB proved pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD sphere square of AC straight line AC THEOR third three plane angles three straight lines tiples touches the circle triangle ABC triangle DEF triplicate ratio twice the rectangle wherefore whole

### Popular passages

Page 173 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 56 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Page 53 - 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 on the line between the points of section, is equal to the square on half the line.

Page 58 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.

Page 94 - 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 23 - Any two sides of a triangle are together greater than the third side.

Page 40 - EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.

Page 103 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square on the line which touches it.

Page 50 - PROP. I. THEOR. If there oe two 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 28 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.