query: Using Ceva's Theorem
positive_passages.docid: 148307
positive_passages.text: Intersection of Altitudes in Hexagon
negative_passages.docid: 31069
negative_passages.text: Smallest and largest values of $\|\vec{v}-\vec{w}\|$
negative_passages.docid: 90373
negative_passages.text: Using Divergence Theorem
negative_passages.docid: 115663
negative_passages.text: Proving an isomorphism using the isomorphism theorems
negative_passages.docid: 139744
negative_passages.text: For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
negative_passages.docid: 81895
negative_passages.text: A generalisation of the fundamental theorem of algebra
negative_passages.docid: 76347
negative_passages.text: Shorter proof for some equvalences
negative_passages.docid: 143801
negative_passages.text: Proving the AGM inequality with 3 variables
negative_passages.docid: 56030
negative_passages.text: Could you prove the theorem?
negative_passages.docid: 135577
negative_passages.text: Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
negative_passages.docid: 148239
negative_passages.text: natural deduction proof with De Morgan's laws
negative_passages.docid: 64629
negative_passages.text: Real Analysis Use of Darboux's Theorem Help
negative_passages.docid: 127052
negative_passages.text: Independence of non-constant real variables
negative_passages.docid: 15365
negative_passages.text: Proving that the triangle inequality holds for a metric on $\mathbb{C}$
negative_passages.docid: 21807
negative_passages.text: on proving bac-cab rule, $\vec{A} \times ( \vec{B} \times \vec{C})= \vec{B} (\vec{A} \cdot\vec{C})- \vec{C}(\vec{A}\cdot\vec{B})$
negative_passages.docid: 141814
negative_passages.text: Proofs using theorems instead of axioms
negative_passages.docid: 55853
negative_passages.text: Proof using Taylor's theorem