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

### From inside the book

Results 1-5 of 19

Page 102

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**common**square of EF , * 3 Ax . and the remaining rectangle AE , EC is therefore equal to the remaining rectangle BE ...**section**of the straight lines AC , DB , draw the diameter GEFH . Now the rectangle AE , EC has been proved ... Page 214

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**common section**of the two planes , are perpen- dicular to the other plane . V. The inclination of a straight line to a plane. Page 215

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**common section**at right angles to it , one upon one plane , and the other upon the other plane . VII . Two planes are said to have the same , or a like incli- nation to one another , which two other planes have , when the said angles ... Page 219

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**common section**is a straight line . Let two planes AB , BC , cut one another , and let the line DB be their**common section**: DB shall be a straight line . If it be not , from the point D to B draw , in the plane AB , the straight ... Page 220

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**common section**of the planes AB , BC cannot but be a straight line . Wherefore , if two planes , & c . Q. E. D. * 4. 1 . PROP . IV . THEOR . If a straight line stand at right angles to each of two straight lines in the point of their ...### Other editions - View all

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

The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |

### 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.